Although we see point-slope and standard form, an equation is usually written in slope-intercept form: y = mx + b. This form allows us to quickly identify the slope (m) and y-intercept (0,b) from looking at the equation. We can manipulate the equation into this format, by solving for y.
Test Objectives:•Demonstrate the ability to write the equation of a line in standard form
•Demonstrate the ability to write the equation of a line in slope-intercept form
•Demonstrate the ability to write the equation of a line in point-slope form
Equations of a Line Test:
#1:
Instructions: Write the slope-intercept form of the equation of each line, given the slope and y-intercept.
a) y-intercept = -2
slope | = | - | 2 |
5 |
b) y-intercept = 1
slope | = | 3 |
4 |
#2:
Instructions: Write the slope-intercept form of the equation of each line, given the slope and y-intercept.
a) y-intercept = 3
slope | = | - | 5 |
4 |
b) y-intercept = 5
slope = -6
#3:
Instructions: Graph each line.
a) y = -2x + 4
b)
y | = | 4x | + | 1 |
5 |
#4:
Instructions: Write each equation using point-slope form, then solve for y and place the equation in slope-intercept form.
a) through (-5,3) : slope = 2
b) through (-1,2) : slope = -3
c) through (0,-5) and (5,2)
#5:
Instructions: Write the standard form of the equation of the line.
a)
y | = | -7x | + | 1 |
3 |
b)
y | = | 1x | + | 3 |
5 |
c)
y | = | -9x | + | 6 |
5 |
Written Solutions:
Solution:
a)
y | = | -2x | - | 2 |
5 |
b)
y | = | 3x | + | 1 |
4 |
Solution:
a)
y | = | -5x | + | 3 |
4 |
b)
y = -6x + 5
Solution:
a)
b)
Solution:
a)
point-slope form: y - 3 = 2(x - (-5))
slope-intercept form: y = 2x + 13
b)
point-slope form: y - 2 = -3(x - (-1))
slope-intercept form: y = -3x - 1
c)
point-slope form: y - 2 = | 7 | (x - 5) |
5 |
slope - intercept form: y = | 7x | - 5 |
5 |
Solution:
a) 7x + 3y = 3
b) x - 5y = -15
c) 9x + 5y = 30