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 addition 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
More on Slope Test:
#1:
Instructions: Write each equation in slope-intercept form, then graph the line.
a) 5x + 2y = -2
#2:
Instructions: Write each equation in slope-intercept form, then graph the line.
a) x + y = 0
#3:
Instructions: Write each equation in slope-intercept form, then graph the line.
a) x + 3y = 9
#4:
Instructions: Determine if each pair of lines are parallel, perpendicular or neither.
a) 8x + 3y = 16 : 3x - 8y = 32
#5:
Instructions: Determine if each pair of lines are parallel, perpendicular or neither.
a) 6x + 7y = 14 : 9x - 2y = -8
Written Solutions:
Solution:
a) $$5x + 2y = -2$$
$$y = -\frac{5}{2}x - 1$$
Solution:
a) x + y = 0
y = -x
Solution:
a) x + 3y = 9
$$y = -\frac{1}{3}x + 3$$
Solution:
a) These lines are perpendicular
$$8x + 3y = 16 : y = -\frac{8}{3}x + \frac{16}{3}$$ $$3x - 8y = 32 : y = \frac{3}{8}x - 4$$ $$-\frac{8}{3} \cdot \frac{3}{8} = -1$$
Solution:
a) These lines are neither parallel nor perpendicular
$$6x + 7y = 14 : y = -\frac{6}{7}x + 2$$ $$9x - 2y = -8 : y = \frac{9}{2}x + 4$$ $$-\frac{6}{7} \cdot \frac{9}{2} \ne -1 : -\frac{6}{7} \ne \frac{9}{2}$$