Exercise 11 Page 293

A linear function is a function whose graph is a non-vertical line. The equation of this type of function follows a specific format, called slope-intercept form. y=mx+b Here, m is the slope and b is the y-intercept of the line. With this information in mind, let's consider the given table of values.

Next, we will plot the points in a coordinate plane and draw the line through them.

Let's find the slope of the line. Recall that the slope m is the ratio of the change in y to the change in x. m=change iny/change inx ⇔ m=y_2-y_1/x_2-x_1 We can use any two points of the line to find the slope. We will arbitrarily use ( 0, 5) and ( 3, 7).

m=y_2-y_1/x_2-x_1

SubstitutePoints

Substitute ( 0,5) & ( 3,7)

m=7- 5/3- 0

SubTerms

Subtract terms

m=2/3

We found that the slope of the line is 23. Let's write a partial equation for our line. y= 2/3x+b Finally, because the line crosses the y-axis at (0, 5), the y-intercept b is 5. y= 2/3x+ 5 Let's add this information to our diagram.