Chapter 4.2, Problem 3CYU

To determine

To find: The equation of line in point-slope form that passes through point $\left(-2,5\right)$ with slope $-6$ .

Answer to Problem 3CYU

The equation of line in point-slope form that passes through point $\left(-2,5\right)$ with slope $-6$ is $y=-6x-7$ .

Explanation of Solution

Given:

A line passes through point $\left(-2,5\right)$ with slope $-6$ .

Concept used:

The formula for equation of line in point-slope form with slope $m$ and point $\left(x_1,y_1\right)$ is:

$y-y_1=m\left(x-x_1\right)$

Calculation:

Replace $\left(x_1,y_1\right)$ as $\left(-2,5\right)$ and $m$ as $-6$ in point-slope form $y-y_1=m\left(x-x_1\right)$ as follows:

$\begin{array}{c}y-5=-6\left(x-\left(-2\right)\right)\\ y-5=-6\left(x+2\right)\\ y=-6x-12+5\\ y=-6x-7\end{array}$

Plot the first given point and then move 6 units downwards and 1 unit towards right to obtain another point. Join to form a line as follows:

Therefore, the equation of line in point-slope form that passes through point $\left(-2,5\right)$ with slope $-6$ is $y=-6x-7$ .