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)`

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)`