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Study Guide Linear equations Mathematics, Grade 8

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LINEAR EQUATIONS Linear equations are equations that have two variables and when graphed are a straight line. Linear equation can be graphed based on their slope and y-intercept. The standard equation for a line is y = mx + b, where m is the slope and b is the y-intercept. Linear equations often have both of the variables on the same side of the equal sign and therefore must be solve for y before it can be graphed. • The slope of the line is the m in the equation y = mx + b. • It is also the rise/run of a line and can be found with the formula (y2 - y1)/(x2 - x1). • The y-intercept of a line is the b in the equation y = mx + b. The y- intercept is the y coordinates of the point where the line crosses the y- axis. • A linear equation can be found in different ways. A linear equation can be found using the slope-intercept form or the point-slope form. How to use linear equations Linear equations when graphed are a straight line. For the x values of a linear equation, there are corresponding y values. The x values and y values are points on the line. • If a linear equation is given, along with certain x values, the y values can be found by substituting in the x values and solving for y. With the linear equation, y = 5x - 2, and the x values, 0, 1, and 2, the y values are -2, 3 and 8. © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.

The slope of a line is the m in the equation y = mx + b. It can be found with the formula m = (y2 - y1)/(x2 - x1), which represents the change in y over the change in x. • Slope is also referred to as the rise over the run. For the linear equation, y = -3x - 2, the slope is -3. • If a linear equation is not in the form y = mx + b, it must be put into that form before finding the slope. • The y-intercept of a line is the b in the equation y = mx + b. The y- intercept is the y coordinate of the point where the line crosses the y- axis. To find the y-intercept a linear equation must be in the form of y = mx + b. • For example, what is the slope and y-intercept of the line 6x -2y = 6? Example: 6x - 2y = 6 -2y = -6x + 6 y = (-6/-2)x +(6/-2) → y = 3x - 3 → the slope is 3; the y-intercept is -3 If the slope and y-intercept are given, the equation of the line can be found by substituting in the equation, y = mx + b. This is called the slope-intercept form. • If the slope and a point are given, the equation of a line can be found by substituting in the equation, y - b = m(x - a), this is called the point-slope form. • For example, what is the equation of a line that has a slope of -8 and goes through the point, (2, -2)? Example: y -b = m(x - a) y - (-2) = -8(x - 2) y + 2 = -8x + 16 → this is the equation of a line in point-slope form • If the slope of a line is given as being parallel to another line, remember that parallel lines have equal slopes. © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.

Try This! 1. What are the y values for the linear equation, 9x + y = 27 when x is 0,1 and 2? 2. What is the slope of a line that goes through the points (5, 4) and (-1, -2)? 3. What are the slope and y-intercept of the line, y = -1/2 x + 6? 4. What are the slope and y-intercept of the line, -8x + 2y = -12? 5. What is the equation of a line that has a slope of -1 and y-intercept of -3 in slope- intercept form? 6. What is the equation of a line that has a slope of 4 and goes through the point (-2, -8) in point-slope form? 7. What is the equation of a line that is parallel to the line y = -4x + 6 and goes through the point (5, -1) in point-slope form? © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.

Linear equations

Mathematics, Grade 8

Linear equations

Study Guide

Linear equations

Flash Cards

Linear equations

Quiz

Linear equations

Worksheets

Linear equations

Games

Study Guide Linear equations Mathematics, Grade 8

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