Slope-intercept form of the equation

Key Concepts: Slope-intercept form of the equation of a line
Martin-Gaye sections and practice problems
3.5: 1 – 51 odd, 53 – 58 all

Example 1
The line 3 x + 2 y = 2 is shown in Figure 1.

a. Find two points on the line and verify that they in fact satisfy the equation 3 x + 2 y = 2 .

b. Find the slope and y-intercept of the line.

c. Solve the equation 3 x + 2 y = 2 for y . State the connection between this new equation and
the slope and y-intercept of the line.

Example 2
The line 4 x − 3 y = 6 is shown in Figure 2.
a. Find two points on the line and verify that they in fact satisfy the equation 4 x − 3 y = 6.
b. Find the slope and y-intercept of the line.
c. Solve the equation 4 x − 3 y = 6 for y . State the connection between this new equation and
the slope and y-intercept of the line.

Definition and most awesome fact
The equation y = m x + b is called the slope-intercept form of a linear equation.
The equation of any non-vertical line can be written in this form. When the equation is written in this
form, the number m is the slope of the line and the point (0,b) is the y-intercept of the line.

Example 3
State the slope and y-intercept of the line with equation
. Graph the line onto Figure 3.

Example 4
State the slope and y-intercept of the line with equation
y = − 4. Graph the line onto Figure 4.

Example 5
State the slope and y-intercept of the line with equation
−3 x − 5 y = 4 . Graph the line onto Figure 5.

Example 6
State the slope and y-intercept of the line with
equation x = − 5. Graph the line onto Figure 6.

Example 7
a. Find an equation for the line in Figure 7.
b. Find an equation for the line parallel to the given line
that passes through the point (6,5).

Example 8
Find an equation for the line shown in Figure 8.

Example 9
Find an equation for the line that passes through the points (−2,3) and (−7,1) .

Example 10
Find an equation for the line that is parallel to the line with equation 6 y = x + 2 and passes
through the point (12, 2) .

Example 11
Find an equation for the line that is perpendicular to the
line in Figure 9 and passes through the point (1,1) .