Exercise 10 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+3y=7

Substitute

y= 0

-3x+3( 0)=7

ZeroPropMult

Zero Property of Multiplication

-3x=7

DivEqn

.LHS /-3.=.RHS /-3.

x=7/-3

MoveNegDenomToFrac

Put minus sign in front of fraction

x=-7/3

An x-intercept of - 73 means that the graph passes through the x-axis at the point ( - 73,0).

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+3y=7

Substitute

x= 0

-3( 0)+3y=7

ZeroPropMult

Zero Property of Multiplication

3y=7

DivEqn

.LHS /3.=.RHS /3.

y=7/3

A y-intercept of 73 means that the graph passes through the y-axis at the point (0, 73).