Chapter 1, Problem 40RE

To determine

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

Answer to Problem 40RE

Thus the slope of the line is $\left[m=\frac{3}{2}\right]$ and $y$ -intercept $[b=0]$ .

  

Explanation of Solution

Given:

  $-\frac{3}{4}x+\frac{1}{2}y=0$

Calculation:

Equation of the line slope-intercept form:

  $y=mx+b$ where $m$ is the slope and $b$ is the $y$ -intercept.

We first write the equation of the given line in slope-intercept form to find its slope.

  $\begin{array}{l}-\frac{3}{4}x+\frac{1}{2}y=0\\ -3x+2y=0\\ \begin{array}{cccc}2y& =3x& & \\ y& =\frac{3}{2}x& y=mx+b& \end{array}\end{array}$

Thus the slope of the line is $\left[m=\frac{3}{2}\right]$ and $y$ -intercept $[b=0]$

The $y$ -intercept is 0 and the point (0,0) is on the graph of the equation, $x$ -intercept is also 0 .

Now we plot the graph.

  

Conclusion:

Thus the slope of the line is $\left[m=\frac{3}{2}\right]$ and $y$ -intercept $[b=0]$ .