Exercise 10 Page 293

A linear function is a function whose graph is a nonvertical 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, 0) and ( 4, -1).

m=y_2-y_1/x_2-x_1

SubstitutePoints

Substitute ( 0,0) & ( 4,-1)

m=-1- 0/4- 0

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Evaluate right-hand side

SubTerms

Subtract terms

m=-1/4

MoveNegNumToFrac

Put minus sign in front of fraction

m=-1/4

We found that the slope of the line is - 14. Let's write a partial equation for our line. y= -1/4x+b Finally, because the line crosses the y-axis at (0, 0), the y-intercept b is 0. y= -1/4x+ 0 ⇔ y= -1/4x Let's add this information to our diagram.