Q21. - Algebra 1

Question

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

$\left(-3,-1\right)$, slope $\frac{2}{5}$

Step-by-Step Solution

Answer

The equation of the line that passes through the point $\left(-3,-1\right)$ and has the slope $\frac{2}{5}$ is $y=\frac{2}{5}x+\frac{1}{5}$. 

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 − 3 , − 1 and has the slope 2 5 .

The slope of the line is $\frac{2}{5}$. Therefore, the value of $m$ is $\frac{2}{5}$.

The given point is $\left(-3,-1\right)$. Therefore, the values of $x_1$ and $y_1$ are $-3$ and $-1$ respectively.

Now substitute $\frac{2}{5}$ for $m$, $-3$ for $x_1$ and $-1$ for $y_1$ in the equation $y-y_1=m\left(x-x_1\right)$ to find the equation of the line.

$$\begin{gathered} y-y_1=m\left(x-x_1\right) \\ y-\left(-1\right)=\frac{2}{5}\left(x-\left(-3\right)\right) \\ y+1=\frac{2}{5}\left(x+3\right) \\ y+1=\frac{2}{5}x+\frac{6}{5} \\ y=\frac{2}{5}x+\frac{6}{5}-1 \\ y=\frac{2}{5}x+\frac{6-5}{5} \\ y=\frac{2}{5}x+\frac{1}{5} \end{gathered}$$

Therefore, the equation of the line that passes through the point $\left(-3,-1\right)$ and has the slope $\frac{2}{5}$ is $y=\frac{2}{5}x+\frac{1}{5}$.