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**4.7 Graphing Lines Using Slope Intercept Form**

Goal: Graph lines in slope intercept form.

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**Slope-Intercept Form of the Linear Equation**

y = mx + b m b = slope = y-intercept Any linear equation which is solved for y is in slope-intercept form.

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**Find the slope and y-intercept of the following linear equations:**

y = -2x - 1 y = 3x + 4 m = -2 b = -1 m = 3 b = 4 -2 1 y = x - y = 5x 9 4 -2 -1 m = m = 5 b = 0 b = 9 4

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**Write a linear equation in the form y = mx + b given the following.**

m = 2, b = -3 y = 2x - 3 m = , b = 5

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**-2 -3 Graph the following linear equation using slope and y-intercept.**

Steps y 1) Find the slope and y-intercept. +3 +2 x 2) Plot the y-intercept. -2 3) Plot the slope. -2 -3 2 m = or m = -3 3 4) Draw line through points.

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**Graph the line which passes through (-2, 1) and has a slope of -3.**

Steps y 1) Plot the point. 2) Write slope as fraction and count off other points. -3 m = -3 -3 x = 1 3 +1 or m = -1 3) Draw line through points.

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**-3 -4 Graph the line which passes through (3, 2) and has a slope of .**

Steps y +4 1) Plot the point. +3 2) Write slope as fraction and count off other points. 3 x m = 4 -3 or m = -4 3) Draw line through points.

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**Write a linear equation in slope-intercept form**

to describe each graph. y = mx + b y y 8 x x -6 2 4 b = -4 b = 3 y = 2x + 3

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**Sometimes we must solve the equation for y before we can graph it.**

The constant, b = 3 is the y-intercept. The coefficient, m = -2 is the slope.

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**1) Plot the y-intercept as a point on the y-axis**

1) Plot the y-intercept as a point on the y-axis. The constant, b = 3, so the y-intercept = 3. down 2 2) Plot more points by counting the slope up the numerator (down if negative) and right the denominator. The coefficient, m = -2, so the slope = -2/1. right 1 down 2 right 1

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**Parallel Lines Graph the following on the coordinate plane.**

y x Parallel lines have the same slope.

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**Lines are parallel! Same slope!**

Tell whether the lines below are parallel. 1) 3x + y = y = -3x + 1 -3x x y = -3x + 7 m = -3 y = mx + b Same slope! m = -3 Lines are parallel!

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