Chapter 1, Problem 39RE

To determine

To find:The slope and y-intercept and graph the line

Answer to Problem 39RE

The slope of the line is $\frac{3}{2}$ and the y-intercept is $\frac{1}{2}$ .

  

Explanation of Solution

Given: $\frac{1}{2}x-\frac{1}{3}y=-\frac{1}{6}$

Formula Used:

Slope-intercept form is $y=mx+b$

Calculation:

Rewrite the equation $\frac{1}{2}x-\frac{1}{3}y=-\frac{1}{6}$ into the form $y=mx+b$ .

Multiply both sides of the equation by 3.

  $3\cdot \frac{1}{2}x-3\cdot \frac{1}{3}y=-3\cdot \frac{1}{6}$

  $\frac{3}{2}x-y=-\frac{1}{2}$

Subtract $\frac{3}{2}x$ from both sides of the equation.

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

  $-y=-\frac{3}{2}x-\frac{1}{2}$

Multiply by -1 on both sides of the equation.

  $\left(-1\right)\left(-y\right)=\left(-1\right)\left(-\frac{3}{2}x\right)-\left(-1\right)\frac{1}{2}$

  $y=\frac{3}{2}x+\frac{1}{2}$

So, the slope of the line is $\frac{3}{2}$ and the y-intercept is $\frac{1}{2}$ .

Since the y-intercept is $\frac{1}{2}$ , a point on the line is $\left(0,\frac{1}{2}\right)$ .

For getting the next point on the line, start form the point $\left(0,\frac{1}{2}\right)$ , move 2 units to the right and then up 3 units. The new points are $\left(2,\frac{7}{2}\right)$ .

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

  

Conclusion:

Therefore, the slope of the line is $\frac{3}{2}$ and the y-intercept is $\frac{1}{2}$ .