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 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
Graphing Slope Intercept Form Practice 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:

#1:

Solutions:

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

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

Graphing a linear equation in two variables

#2:

Solutions:

a) x + y = 0

y = -x

Graphing a linear equation in two variables

#3:

Solutions:

a) x + 3y = 9

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

Graphing a linear equation in two variables

#4:

Solutions:

a) These lines are perpendicular

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


#5:

Solutions:

a) These lines are neither parallel nor perpendicular

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