Chapter 1.1, Problem 28E

To determine

Calculate the equation of the line that passes through the given points and the indicated slopes.Also,draw the graph of the line.

Answer to Problem 28E

The equation of the line is $3x-4y=14$ .

Explanation of Solution

Given:

It is given in the question that the coordinate and the slopes are $(-2,-5)$ and $m=\frac{3}{4}$ .

Concept Used:

In this,it has to be use the concept of point − slope form and the formula used is $y-y_1=m(x-x_1)$ .

Calculation:

Now , use the $(-2,-5)$ and $m=\frac{3}{4}$ .

By using the point − slope line equation , put into $(x_1,y_1)$ and the slope into m.

  $\begin{array}{l}y-y_1=m(x-x_1)\\ y=m(x-x_1)+y_1\\ y=\frac{3}{4}(x-(-2))+(-5)\\ 4y=3x+6-20\\ 4y=3x-14\end{array}$

The general form is $Ax+By=C$ .Get the x and y terms all to one side

  $\begin{array}{l}4y=3x-14\\ -3x+4y=-14\\ 3x-4y=14\end{array}$

To graph the line, calculate one other point at $x=1$

  $\begin{array}{l}4y=3(1)-14\\ y=-\frac{11}{4}\end{array}$

Now, plot the two points and draw a straight line through them.

  

Conclusion:

The equation is $3x-4y=14$ .