Chapter 14.4, Problem 1AYU

Find an equation of the line with slope 5 containing the point $\left(2,-4\right).\left(\text{p }\text{. 33}\right)$

To determine

To find: The equation of the line with slope 5 containing the point $\left(2,-4\right)$.

Answer to Problem 1AYU

Solution:

$y=5x-14$

Explanation of Solution

Given:

Slope of the line: 5.

Point: $\left(2,-4\right)$.

Formula used:

We know the equation of the line with slope m and containing the point $\left(a,b\right)$ is: $y-b=m\left(x-a\right)$.

Calculation:

Here the slope of the line is 5, ie, $m=5$ and the point is $\left(2,-4\right)$, ie, $\left(a,b\right)=\left(2,-4\right)$.

Therefore the equation of the line will be:

$y-\left(-4\right)=5\left(x-2\right)$

$y+4=5x-10$

$y+4-4=5x-10-4$

$y=5x-14$

Hence the equation of the line is $y=5x-14$.