Chapter CR, Problem 1E

Write an equation of the line with slope – 4 and containing the point $\left(-7,1\right)$.

To determine

To calculate: The equation of the line with slope $-4$ and containing the point $\left(-7,1\right)$.

Answer to Problem 1E

Solution:

The equation of the line is $y=-4x-27$.

Explanation of Solution

Given information:

The slope of the line is $-4$ and contains the point $\left(-7,1\right)$.

Formula used:

Equation of the line with given slope $m$ and a passing point $\left(x_1,y_1\right)$:

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

Calculation:

Consider a line with the slope $-4$ and passing through the point $\left(-7,1\right)$.

Recall the equation of the line with given slope $m$ and a passing point $\left(x_1,y_1\right)$:

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

Substitute $m$ as $-4$ and $\left(x_1,y_1\right)$ as $\left(-7,1\right)$ in this equation to get the required equation of line:

$\begin{array}{c}\left(y-y_1\right)=m\left(x-x_1\right)\\ \left(y-1\right)=-4\cdot \left(x-\left(-7\right)\right)\\ y-1=-4x-28\\ y=-4x-28+1\end{array}$

Further simplify to get:

$\begin{array}{c}y=-4x-28+1\\ y=-4x-27\end{array}$

Thus, the required equation of line is $y=-4x-27$.