Q20. - Algebra 1

Question

Write an equation of the line that passes through the given point and has the given slope.

$\left(2,-6\right)$, slope $-4$

Step-by-Step Solution

Answer

The equation of the line that passes through the point $\left(2,-6\right)$ and has the slope $-4$ is $y=-4x+2$. 

Step 1. Write the equation of the line that passes through the point x 1 , y 1 and has the slope m .

The equation of the line that passes through the point $\left(x_1,y_1\right)$ and has the slope $m$ is given by:

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

Step 2. Write the equation of the line that passes through the point 2 , − 6 and has the slope − 4 .

The slope of the line is $-4$. Therefore, the value of $m$ is $-4$.

The given point is $\left(2,-6\right)$. Therefore, the values of $x_1$ and $y_1$ are 2 and $-6$ respectively.

Now substitute $-4$ for $m$, 2 for $x_1$ and $-6$ for $y_1$ in the equation $y-y_1=m\left(x-x_1\right)$ to find the equation of the line.

$$\begin{gathered} y-y_1=m\left(x-x_1\right) \\ y-\left(-6\right)=-4\left(x-2\right) \\ y+6=-4x+8 \\ y=-4x+8-6 \\ y=-4x+2 \end{gathered}$$

Therefore, the equation of the line that passes through the point $\left(2,-6\right)$ and has the slope $-4$ is $y=-4x+2$.