Linear Functions

6.4 Slope-Intercept Form of the Equation for a Linear Function

Vocabulary• Slope-intercept form• The equation of a line in the form where m is the

slope and b is the y-intercept• General form• The equation of a line in the form where A, B, and

C are integers

Equations of a Linear Function

• We can make an equation that describes a line’s location on a graph. This is called a linear equation. There are three forms of linear equation that we will be looking at:• Standard Form: Ax + By + C = 0, where A, B, and C

are integers.• Slope-intercept form: y = mx + b, where m is the

slope, and b is the y-intercept. • Slope-point form: y – y1 = m(x – x1), where m is the

slope, and the line passes through a point located at (x1, y1)• Today we will look at the first two forms.

Slope-intercept form• In general, any linear function can be described in

slope-intercept form.• When graphing lines, the slope-intercept form is

useful because all the information you need to graph the line is found in the equation.• If we know the slope of the line, and the y-intercept,

we can graph the line by using the following steps:Step 1) Plot the y-interceptStep 2) From the y-intercept, count the rise and the run.Step 3) Draw a line through both points.

The graph of a linear function has slope 3/5 and y-intercept -4.Write an equation for this function.

y = 3/5x - 4

The graph of a linear function has a slope -7/3 and y-intercept 5.Write an equation for this function.

y = -7/3x + 5

Slope-intercept form

Graph the linear equation

𝑦=−12𝑥+3

Step 1) Plot the y-interceptStep 2) From the y-intercept, count the rise and the run.Step 3) Draw a line through both points.

Rise=-1

Run=2

(0,3)

Graph the Equationy = 2x – 7

y-intercept is -7

slope is 2

Writing an equation for a given graph

• In certain cases, we will be asked to write the equation of a line given its graph. Look at the following example:

y-intercept = -4Find another point on the line that is easily read from the graph.Count out the rise and the run between the two points.

(-2,-1)

Rise= -3

Run=2 y = -3/2x - 4

Practice

Write an equation to describe this function.

y = -2/3x - 2

PracticeThe student council sponsored a Christmas dance. A ticket cost $5 and the cost for the DJ was $300.

Write an equation for the profit (P) in dollars, on the sale of tickets (t).Suppose 123 people bought tickets. What was the profit?Suppose the profit was $350. How many people bought tickets?Could the profit be exactly $146?

SolutionProfit is income subtract expenses.

Use the equation:P = 5(123) – 300P = 615 – 300P = $315

350 = 5t – 300650 = 5t130 = t

146 = 5t – 300446 = 5t89.2 = t Can’t sell a fraction of a ticket.

P = 5t - 300