5.1 Slope-Intercept FormOBJECTIVE 1 : Use slope-intercept form to write an

equation of a line.

Slope-Intercept Form:

The slope-intercept form of the equation of a line with slope m and y-intercept b is

y = mx + b

If you are given or can determine the slope and y-intercept of a line, you can write the equation in slope-intercept form.

2. Substitute the slope for m and the y-intercept for b.

Steps to write equation in Slope-Intercept Form:

EXAMPLE

y = 3x + (– 4)

y = 3x – 4

Write the equation of the line whose slope is 3 and whose y-intercept is –4

1. Determine the slope and y-intercept.

m = 3, b = –4

EXAMPLE

Write the equation of a line with the slope of -4 and the y-intercept of 5.

m = - 4 b = 5

y = mx + b

y = - 4x + 5

EXAMPLE

2. y = mx + b

3. y = 5x + (– 2)

4. y = 5x – 2

Write the equation of the line shown in the graph using slope-intercept form.

1. Use two points on the graph to determine slope.

51

5

m

Use the graph to determine the y-intercept.

2b

+5

+1

EXAMPLE

Write the equation of the line shown on the graph in slope-intercept form.

y –intercept

(0,3)Slope: m =

+3

+2

2

3

=2

3

y = mx + b

y = 2

3x + 3

b = 3

Slope

OBJECTIVE 2: Model a real-life situation with a linear function.

EXAMPLE

The number of trout in a lake was estimated at 45 thousand in 1995. During the next 10 years, the trout population is expected to increase by about 3 thousand per year.

1. Identify the b ( the starting point)

b = 45,000

2. Identify the m ( the rate of change)

m = 3000

3. Write the equation in slope-intercept form.

y = 3000x + 45,000

EXAMPLE

A plumber charges $66 for the service call and $45 for each hour. Write the linear model to reflect the plumber’s charges. Use the equation to determine the cost of a 3 hour service call.

1. Identify b ( the starting point)b = 66

2. Identify m (the rate of change)

m = 45

3. Write the equation.y = 45x + 66

4. Let x = 3 and substitute into the equation.

y = 45(3) + 66y = 135 + 66

Y =201 $201