Question

use the given conditions to write an equation for the line in point - slope form and in slope - intercept form. passing through (-7,-5) and parallel to the line whose equation is y = - 3x + 1 write an equation for the line in point - slope form. y + 5 = - 3(x + 7) (simplify your answer. use integers or fractions for any numbers in the equation.) write an equation for the line in slope - intercept form. (simplify your answer. use integers or fractions for any numbers in the equation.)

Explanation:

Step1: Recall slope - intercept form

The slope - intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. The given line is $y=-3x + 1$, so its slope $m=-3$. Parallel lines have the same slope.

Step2: Start with point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$, where $(x_1,y_1)$ is a point on the line and $m$ is the slope. We have the point $(-7,-5)$ and $m = - 3$, so the point - slope form is $y+5=-3(x + 7)$.

Step3: Convert to slope - intercept form

Expand the right - hand side of the point - slope equation:
\[

$$\begin{align*} y+5&=-3(x + 7)\\ y+5&=-3x-21 \end{align*}$$

\]
Then, isolate $y$ by subtracting 5 from both sides:
\[

$$\begin{align*} y&=-3x-21 - 5\\ y&=-3x-26 \end{align*}$$

\]

Answer:

$y=-3x - 26$