Exercise 14 Page 177

We will graph the following equation by finding its intercepts. 9y=3x+18

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 given equation, we will substitute 0 for y and solve for x.

9y=3x+18

Substitute

y= 0

9( 0)=3x+18

ZeroPropMult

Zero Property of Multiplication

0=3x+18

SubEqn

LHS-3x=RHS-3x

-3x=18

DivEqn

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

x=-6

The x-intercept is the point (-6,0). Let's continue with the y-intercept.

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.

9y=3x+18

Substitute

x= 0

9y=3( 0)+18

ZeroPropMult

Zero Property of Multiplication

9y=18

DivEqn

.LHS /9.=.RHS /9.

y=2

Thus, the point (0,2) is the y-intercept.

Graphing the line

Now, we will plot the intercepts on a coordinate plane and connect them with a straight line.