Exercise 11 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.

3x-5y=-20

Substitute

y= 0

3x-5( 0)=-20

ZeroPropMult

Zero Property of Multiplication

3x=-20

DivEqn

.LHS /3.=.RHS /3.

x=-20/3

MoveNegNumToFrac

Put minus sign in front of fraction

x=-20/3

An x-intercept of - 203 means that the graph passes through the x-axis at the point ( - 203,0).

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.

3x-5y=-20

Substitute

x= 0

3( 0)-5y=-20

ZeroPropMult

Zero Property of Multiplication

-5y=-20

DivEqn

.LHS /(-5).=.RHS /(-5).

y=4

A y-intercept of 4 means that the graph passes through the y-axis at the point (0, 4).