Question

Write an equation in slope-intercept form for the line that passes through the given point and is parallel to the graph of each equation.

$\left(-5,1\right)$,$y=-3x+2$

Short answer

The required equation is represented by $y=-3x-14$.

Step-by-step solution

Step 1. Determine the slope of provided equation.

Take the help of the standard form $y=mx+c$ in which the representation of the slope is m so compare this equation with the provided equation.

$m=-3$

Step 2. Determine the required equation.

Take the help of obtained standard form represented by $y-y_1=m\left(x-x_1\right)$in which the required values can be filled by using the obtained slope because both the lines are having a parallel relation so their slope will be the same and take provided point as it is in the form of $\left(x_1,y_1\right)$.

$$\begin{gathered} y-1=-3\left(x-\left(-5\right)\right) \\ y-1=-3x-15 \\ y=-3x-14 \end{gathered}$$

Step 3. Write the conclusion.

The obtained equation is$y=-3x-14$ so it is the required equation.