Chapter 1, Problem 43RE

To determine

To find: The x-intercepts and y-intercepts.

Answer to Problem 43RE

Thex-intercept is 4 and y-intercept is 6.

Explanation of Solution

Given: $\frac{1}{2}x-\frac{1}{3}y=2$

Calculation:

For obtaining the x-intercept, let y = 0 in the equation and solve for x.

  $\frac{1}{2}x+\frac{1}{3}y=2$

  $\frac{1}{2}x+\frac{1}{3}\left(0\right)=2$

  $\frac{1}{2}x=2$

Multiply by 2 on both sides of the equation.

  $2\cdot \frac{1}{2}x=2\cdot 2$

  $x=4$

So, the x-intercept is 4 and a point on the graph of the equation is $\left(4,0\right)$ .

For obtaining the y-intercept, let x = 0 in the equation and solve for x.

  $\frac{1}{2}x+\frac{1}{3}y=2$

  $\frac{1}{2}\left(0\right)+\frac{1}{3}y=2$

  $\frac{1}{3}y=2$

Multiply by 3 on both sides of the equation.

  $3\cdot \frac{1}{3}y=3\cdot 2$

  $y=6$

So, the y-intercept is 6 and a point on the graph of the equation is $\left(0,6\right)$ .

The line can be graphed by plotting the points and drawing a line passing through them.

  

Conclusion:

Therefore, the x-intercept is 4 and y-intercept is 6.