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

Vocabulary

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 – y 1 = m(x – x 1 ), where m is the slope, and the line passes through a point located at (x 1, y 1 ) 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-intercept Step 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

Graph the linear equation Step 1) Plot the y-intercept Step 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 Equation y = 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 = -4 Find 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

Practice The 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?

Solution Profit is income subtract expenses. Use the equation: P = 5(123) – 300 P = 615 – 300 P = $ = 5t – = 5t 130 = t 146 = 5t – = 5t 89.2 = t Can’t sell a fraction of a ticket. P = 5t - 300