Question

A line has the equation `2y=-3x+1`, how do you find an equation of a line parallel to this line that has a y intercept of -2?

Answer 1

See the process for solving this problem below in the Explanation:

Explanation:

First, we need to put the line from the problem in the slope-intercept form by solving for `y`:

`(2y)/color(red)(2) = (-3x + 1)/color(red)(2)`

`(color(red)(cancel(color(black)(2)))y)/cancel(color(red)(2)) = -3/2x + 1/2`

`y = -3/2x + 1/2`

The slope-intercept form of a linear equation is:

`y = color(red)(m)x + color(blue)(b)`

Where `color(red)(m)` is the slope and `color(blue)(b` is the y-intercept value.

So we know the slope of the line from the question is `-3/2`

And, a parallel line by definition has the same slope so the slope of the line we are looking for also has a slope of `-3/2`

And because we know the `y` intercept, `-2`, we can substitute both these values into the slope-intercept formula to find the equation we are looking for:

`y = color(red)(-3/2)x + color(blue)(-2)`

`y = color(red)(-3/2)x - color(blue)(2)`