### About Graphing Slope Intercept Form:

We can graph a line very quickly by placing the equation in slope-intercept form: y = mx + b. This allows us to plot one point, the y-intercept, and any additional points using the slope, given as m. Using slope, we can also determine if two lines are parallel, perpendicular, or neither.

Test Objectives

- Demonstrate the ability to graph a line using one point and the slope
- Demonstrate the ability to determine if two lines are parallel
- Demonstrate the ability to determine if two lines are perpendicular

#1:

Instructions: Write each equation in slope-intercept form, then graph the line.

a) 5x + 2y = -2

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#2:

Instructions: Write each equation in slope-intercept form, then graph the line.

a) x + y = 0

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#3:

Instructions: Write each equation in slope-intercept form, then graph the line.

a) x + 3y = 9

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#4:

Instructions: Determine if each pair of lines are parallel, perpendicular or neither.

a) 8x + 3y = 16 : 3x - 8y = 32

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#5:

Instructions: Determine if each pair of lines are parallel, perpendicular or neither.

a) 6x + 7y = 14 : 9x - 2y = -8

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Written Solutions:

#1:

Solutions:

a) $$5x + 2y=-2$$

$$y=-\frac{5}{2}x - 1$$

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#2:

Solutions:

a) x + y = 0

y = -x

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#3:

Solutions:

a) x + 3y = 9

$$y=-\frac{1}{3}x + 3$$

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#4:

Solutions:

a) These lines are perpendicular

$$8x + 3y=16 : y=-\frac{8}{3}x + \frac{16}{3}$$ $$3x - 8y=32 : y=\frac{3}{8}x - 4$$ $$-\frac{8}{3}\cdot \frac{3}{8}=-1$$

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#5:

Solutions:

a) These lines are neither parallel nor perpendicular

$$6x + 7y=14 : y=-\frac{6}{7}x + 2$$ $$9x - 2y=-8 : y=\frac{9}{2}x + 4$$ $$-\frac{6}{7}\cdot \frac{9}{2}\ne -1 : -\frac{6}{7}\ne \frac{9}{2}$$