Chapter 1.4, Problem 2CFU

To determine

To find: the equation of line in two different ways.

Answer to Problem 2CFU

  $y=\frac{1}{4}x-4\frac{3}{4}$

Explanation of Solution

Given information:

Slope, $m=\frac{1}{4}$

Point on line (x,y) = $\left(3,-4\right)$

Calculation

First Method: Using slope intercept formula. $y=mx+b$

Substitute, point coordinate and value of m in the slope intercept formula, to get

  $\begin{array}{c}-4=\frac{1}{4}\left(3\right)+b\\ b=-4-\frac{3}{4}\\ b=\frac{-16-3}{4}\\ b=\frac{-19}{4}\\ b=-4\frac{3}{4}\end{array}$

Substitute the value of b and m in the slope intercept formula to get the equation of line as follows:

  $y=\frac{1}{4}x-4\frac{3}{4}$

Second Method: Using point slope formula. $y-y_1=m\left(x-x_1\right)$

Substitute, point coordinate and value of m in the point slope formula, to get

  $\begin{array}{c}y-\left(-4\right)=\left(\frac{1}{4}\right)\left(x-3\right)\\ y+4=\left(\frac{1}{4}\right)\left(x-3\right)\end{array}$

Put $x=0$ , to solve y-intercept as follows:

  $\begin{array}{c}y+4=\left(\frac{1}{4}\right)\left(0-3\right)\\ y+4=-\frac{3}{4}\\ y=\frac{3}{4}-4\\ =\frac{-3-16}{4}\\ =\frac{-19}{4}\\ =-4\frac{3}{4}\end{array}$

Substitute the y-intercept, and value of m in the point slope formula, to get

  $y=\frac{1}{4}x-4\frac{3}{4}$

Thus, the line equation by point slope method is , $y=\frac{1}{4}x-4\frac{3}{4}$