Question

instruction: write the equation of the line that... goes through the point (2, -3) and runs parallel to the line. y = -3x - 4. step 1: identify the slope of the given line and its parallel slope. step 2: use point - slope form. y - y1 = m(x - x1) step 3: convert to slope - intercept form (optional)

Explanation:

Step1: Identify slope

The given line is $y = - 3x-4$, its slope $m=-3$. Parallel lines have equal slopes, so the slope of the required line is also $m=-3$.

Step2: Apply point - slope form

The point - slope form is $y - y_1=m(x - x_1)$, where $(x_1,y_1)=(2,-3)$ and $m = - 3$. Substitute these values: $y-(-3)=-3(x - 2)$.

Step3: Convert to slope - intercept form

Simplify the point - slope equation:
\[

$$\begin{align*} y + 3&=-3x+6\\ y&=-3x + 6-3\\ y&=-3x+3 \end{align*}$$

\]

Answer:

$y=-3x + 3$