Illustrative Math Alignment: Grade 8 Unit 3

Topic

The Point-Slope Form

Description

In this example, we explore finding the equation of a line with a slope of -1 passing through the point (5, 2). Applying the point-slope formula y - y1 = m(x - x1), we substitute the given values to obtain y - 2 = -(x - 5). After simplification, the final equation of the line is y = -x + 7.

Topic

The Point-Slope Form

Description

This example demonstrates the application of the point-slope formula to find the equation of a line with a slope of 3 passing through the point (-2, 7). Using the formula y - y1 = m(x - x1), we substitute the given values to get y - 7 = 3(x - (-2)). After simplification, the resulting equation is y = 3x + 13.

Topic

The Point-Slope Form

Description

In this example, we explore finding the equation of a line with a slope of -5 that passes through the point (-7, 5). Applying the point-slope formula y - y1 = m(x - x1), we substitute the given values to obtain y - 5 = -5(x - (-7)). After simplification, the final equation of the line is y = -5x - 30.

Topic

The Point-Slope Form

Description

This example demonstrates the application of the point-slope formula to find the equation of a line with a slope of 2 passing through the point (-2, -3). Using the formula y - y1 = m(x - x1), we substitute the given values to get y - (-3) = 2(x - (-2)). After simplification, the resulting equation is y = 2x + 1.

Topic

The Point-Slope Form

Description

This example demonstrates the application of the point-slope formula to find the equation of a line with a slope of -7 passing through the point (-8, -5). Using the formula y - y1 = m(x - x1), we substitute the given values to get y - (-5) = -7(x - (-8)). After simplification, the resulting equation is y = -7x - 61.

Topic

The Point-Slope Form

Description

In this example, we explore finding the equation of a line with a slope of 4 passing through the point (8, -2). Applying the point-slope formula y - y1 = m(x - x1), we substitute the given values to obtain y - (-2) = 4(x - 8). After simplification, the final equation of the line is y = 4x - 34.

Topic

The Point-Slope Form

Description

This example demonstrates the application of the point-slope formula to find the equation of a line with a slope of -2 passing through the point (3, -8). Using the formula y - y1 = m(x - x1), we substitute the given values to get y - (-8) = -2(x - 3). After simplification, the resulting equation is y = -2x - 2.

In this set of math examples, see how slope is calculated for a staircase based on measures for the rise and the run.

This Teacher's Guide provides an overview of the 12 worked-out examples that show how to find the equation of a line, given two points.

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This Teacher's Guide provides an overview of the 13 worked-out examples that show how to graph a linear function, given the slope and y-intercept.

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This Teacher's Guide provides an overview of the 20 worked-out examples that show how to use the Midpont Formula.

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This Teacher's Guide provides an overview of the 8 worked-out examples that show how to find the equation of a lineusing the Point Slope Form.

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This Teacher's Guide provides an overview of the 21 worked-out examples that show how to use the Slope Formula.

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The complete set of 21 examples that make up this set of tutorials. NOTE: The download is a PPT file.

This is part of a collection of math quizzes on the topic of finding the Equation of a Line Given Two Points.

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This is part of a collection of math quizzes on the topic of finding the Equation of a Line Given Two Points.

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ary">click on this link.

This is part of a collection of math quizzes on the topic of finding the Equation of a Line Given Two Points.

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This is part of a collection of math quizzes on the topic of Linear Equations.

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This is part of a collection of math quizzes on the topic of Linear Equations.

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This is part of a collection of math quizzes on the topic of Linear Equations.

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This is part of a collection of math quizzes on the topic of the Slope Formula.

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This is part of a collection of math quizzes on the topic of the Slope Formula.

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This is part of a collection of math quizzes on the topic of the Slope Formula.

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Written and hosted by internationally acclaimed math educator Dr. Monica Neagoy, this video introduces students to systems of linear equations in two or three unknowns. To solve these systems, the host illustrates a variety of methods: four involve the TI-Nspire (spreadsheet, graphs and geometry, matrices and nSolve) and two are the classic algebraic methods known as substitution and elimination, also called the linear combinations method. The video ends with a summary of the three possible types of solutions. Concepts explored: equations, linear equations, linear systems Note: The download for this resources is the Promethean Flipchart.

To access the full video [Algebra Nspirations: Solving Systems of Equations]: https://media4math.com/library/algebra-nspirations-solving-systems-equations

In this set of Quizlet flash cards test understanding of nonlinear systems.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

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Find the slope of the line connecting two points in this 20-flash card set. The integers are in the range -20 to 20.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

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Find the slope of the line connecting two points in this 20-flash card set. The integers are in the range -20 to 20.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

Find the slope of the line connecting two points in this 20-flash card set. The integers are in the range -20 to 20.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

Find the slope of the line connecting two points in this 20-flash card set. The integers are in the range -20 to 20.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

Find the slope of the line connecting two points in this 20-flash card set. The integers are in the range -20 to 20.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

Find the slope of the line connecting two points in this 20-flash card set. The integers are in the range -20 to 20.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

Find the slope of the line connecting two points in this 20-flash card set. The integers are in the range -20 to 20.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

Find the slope of the line connecting two points in this 20-flash card set. The integers are in the range -20 to 20.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

Find the slope of the line connecting two points in this 20-flash card set. The integers are in the range -20 to 20.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

Find the slope of the line connecting two points in this 20-flash card set. The integers are in the range -20 to 20.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

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In this set of Quizlet flash cards test understanding of solving systems using the elimination method.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

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In this set of Quizlet flash cards test understanding of solving systems using the substitution method.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

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In this set of Quizlet flash cards test understanding of linear systems.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

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Topic

Linear Functions

Description

The term is "Linear Function," defined as a function of the form y = mx + b, where m is the slope of the line and b is the y-intercept. This term provides the basic definition of linear functions, integral to understanding their behavior and applications.

Topic

Linear Functions

Description

The term is "y-Intercept," defined as the point on the y-axis where a linear function intersects. In slope-intercept form, it is designated as b in y = mx + b. This term complements the x-intercept by focusing on the vertical axis, completing the understanding of graph interactions.

Topic

Linear Functions

Description

The term is "x-Intercept," defined as the point on the x-axis where a linear function intersects, calculated as x = -b/m when y = 0 in the equation y = mx + b. This term provides insight into the graphical representation of linear functions and their interaction with the x-axis.

Topic

Linear Functions

Description

The term is "Rate of Change," defined as the slope, interpreted as the rate at which the dependent variable changes relative to the independent variable. An example is speed as a rate of change of distance over time. This term highlights the application of slope in real-world scenarios, making the concept more tangible and relatable.

Topic

Linear Functions

Description

The term is "Equations of Perpendicular Lines," defined as two linear functions with graphs that are perpendicular. Their slopes are negative reciprocals, represented as y1 = mx + b1 and y2 = -1/m * x + b2. This term explores the relationship between slopes of perpendicular lines, deepening understanding of linear graph orientations.

Topic

Linear Functions

Description

The term is "Equations of Parallel Lines," defined as two linear functions with parallel graphs that have the same slope but different y-intercepts. Represented as y1 = mx + b1 and y2 = mx + b2, where m is the slope. This term explains the geometric relationship of parallel lines, reinforcing the role of slope in linear functions.

Topic

Linear Functions

Description

The term is "Linear Equation in Standard Form," defined as a linear equation with two variables and three constant terms, represented as Ax + By = C where A and B are not equal to zero. This term sets the stage for converting between forms of linear equations, essential for solving and graphing.

Topic

Linear Functions

Description

The term is "Converting from Standard Form to Slope-Intercept Form," defined as rewriting a linear equation in the form y = mx + b using the constants from the standard form Ax + By = C. The conversion formula is y = -A/B * x + C/B. This term is crucial for transitioning between different representations of linear equations, enabling easier analysis and graphing.

Topic

Linear Functions

Description

The term is "Direct Variation," defined as a linear function of the form y = kx, where k is the constant of variation. Graphs of direct variations cross the origin, and the constant of variation is the slope of the graph. This term emphasizes proportional relationships in linear functions, highlighting their simplicity and graphical characteristics.

Topic

Linear Functions

Description

The term is "Line of Best Fit," defined as a linear function that serves as a model for a set of scatterplot data. It helps represent the central trend of data points. This term enhances understanding of linear functions in the context of data analysis and graphical trends.

Topic

Linear Functions

Description

The term is "Slope of a Line," defined as the ratio of the rise over the run, or the change in vertical distance over the change in horizontal distance. Represented as m in the equation y = mx + b. This term is a fundamental component of linear equations, providing a measure of steepness and direction.