Exercise 12 Page 326

To determine the x- and y-intercepts of a line, we need to substitute 0 for one variable, solve, then repeat for the other variable.

Finding the x-intercept

Think of the point where the graph of an equation crosses the x-axis. The y-value of that ( x, y) coordinate pair is 0, and the x-value is the x-intercept. To find the x-intercept of the equation, we should substitute 0 for y and solve for x.

7x-y=21

Substitute

y= 0

7x- 0=21

SubTerm

Subtract term

7x=21

DivEqn

.LHS /7.=.RHS /7.

x=3

An x-intercept of 3 means that the graph passes through the x-axis at the point ( 3,0).

Finding the y-intercept

Let's use the same concept to find the y-intercept. Consider the point where the graph of the equation crosses the y-axis. The x-value of the ( x, y) coordinate pair at the y-intercept is 0. Therefore, substituting 0 for x will give us the y-intercept.

7x-y=21

Substitute

x= 0

7( 0)-y=21

ZeroPropMult

Zero Property of Multiplication

- y=21

MultEqn

LHS * (-1)=RHS* (-1)

y=-21

A y-intercept of -21 means that the graph passes through the y-axis at the point (0, -21).