Exercise 3 Page 177

To determine the x-intercept for the given equation, we will substitute 0 for y and solve for x. To determine the y-intercept, we will substitute 0 for x and solve for y.

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 equal to 0, and the x-value is the x-intercept. Consider the given equation. 2x-3y=-6Let's substitute 0 for y and solve for x.

2x-3y=-6

Substitute

y= 0

2x-3( 0)=-6

ZeroPropMult

Zero Property of Multiplication

2x=-6

DivEqn

.LHS /2.=.RHS /2.

x=-3

The x-intercept of the equation is -3.

Finding the y-intercept

In the same way as above, now 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.

2x-3y=-6

Substitute

x= 0

2( 0)-3y=-6

ZeroPropMult

Zero Property of Multiplication

-3y=-6

DivEqn

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

y=2

The y-intercept of the equation is 2.