Question

Find the equation of the line passing through the point (2, -4) that is parallel to the line y=3x+2​

Answer 1

Answer (assuming it can be put in point-slope format):

$y + 4 = 3(x-2)$

Step-by-step explanation:

You can write an equation of a line when knowing its slope and a line it passes through using point slope formula, $y-y_1 = m (x-x_1)$.

1) First, find the slope of the equation. We know it has to be parallel to y = 3x + 2. Lines that are parallel have the same slope, thus the slope of y = 3x + 2 is the slope of the answer as well. y = 3x + 2 is in slope-intercept format, or $y = mx + b$. The coefficient of the x term, or $m$, represents the slope - so, the slope must be 3.

2) Now, use point-slope formula,$y-y_1 = m (x-x_1)$,  to write the equation. Substitute $m$, $x_1$, and $y_1$ for real values.

The $m$ represents the slope, so substitute 3 for $m$. The $x_1$ and $y_1$ represent the x and y values of a point the line crosses through. The line crosses through (2, -4), so substitute 2 for $x_1$ and -4 for $y_1$. This gives the following answer:

$y - (-4) = 3 (x-(2))\\y + 4 = 3(x-2)$