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