Chapter 1, Problem 38RE

To determine

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

Answer to Problem 38RE

Thus the slope of the line is $\left[m=-\frac{3}{4}\right]$ and $y$ -intercept is $[b=3]$

  

Explanation of Solution

Given:

  $3x+4y=12$

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.

  $\begin{array}{cccc}3x+4y& =12& & \\ 4y& =-3x+12& & \\ y& =-\frac{3}{4}x+3& y=mx+b& \end{array}$

Thus the slope of the line is $\left[m=-\frac{3}{4}\right]$ and $y$ -intercept $[b=3]$

The $y$ -intercept is 3 and the point (0,3) is on the graph of the equation.

  $y=-\frac{3}{4}x+3$

To obtain second point on the graph, let $x=4$ in the equation and solve for $y$ .

  $\begin{array}{l}y=-\frac{3}{4}\cdot 4+3\\ y=0\end{array}$

Thus the second point on the graph is (4,0)

We plot the points (0,3) and (4,0) on the Cartesian plane and draw a line though the points.

  

Conclusion:

Thus the slope of the line is $\left[m=-\frac{3}{4}\right]$ and $y$ -intercept $[b=3]$ .