First, use the given points to calculate the slope.
Then, identify the y-intercept.
B
Recall the meaning of R and A.
A
Equation: R=2A+2 Graph:
B
See solution.
Practice makes perfect
We are given a table that shows the revenue R in millions of dollars of a company when it spends A millions of dollars on advertising.
Advertising, A
0
2
4
6
8
Revenue, R
2
6
10
14
18
We want to write a function that relates R to A. To do so, recall that functions written in slope-intercept form follow a specific format.
y= mx+ b
Here, m represents the slope and b the y-intercept. In our case, R represents y and x indicates A. To find the slope we can use the slope formula.
m = y_2-y_1/x_2-x_1
We will substitute the points ( 0, 2) and ( 2, 6) into the formula and calculate the slope.
The y-intercept is the value of y when the line crosses the y-axis. It will occurs when x=0. From the table, we can see that when x=0 the value of y is 2. Then, the y-intercept is equal to 2. Now we can write the function substituting the obtained values into the slope-intercept form.
R= 2A+ 2
Finally, let's draw the given points on a coordinate plane and draw a line that passes through them.
Since A represents the price of advertising and R the revenue, the slope of the function indicates that the amount of spending on advertising increases 2 million dollars. The y-intercept indicates that the revenue begins to increase from the 2 millon dollars.
