Question

What is the equation of a line that goes through `(-5,1)` and is parallel to `y = -3/5x + 4`?

Answer 1

See a solution process below:

Explanation:

The equation of the line from the problem is in slope-intercept for. 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.

`y = color(red)(-3/5)x + color(blue)(4)`

A parallel line will have the same slope as the line it is parallel to. Therefore the slope of the line we are looking for is:

`color(red)(-3/5)`

We can use the point-slope formula to write an equation of the line. The point-slope formula states: `(y - color(red)(y_1)) = color(blue)(m)(x - color(red)(x_1))`

Where `color(blue)(m)` is the slope and `color(red)(((x_1, y_1)))` is a point the line passes through.

Substituting the slope from the line in the problem and the value of the points in the problem gives:

`(y - color(red)(1)) = color(blue)(-3/5)(x - color(red)(-5))`

`(y - color(red)(1)) = color(blue)(-3/5)(x + color(red)(5))`

We can now solve to transform this equation to the slope-intercept form:

`y - color(red)(1) = (color(blue)(-3/5) xx x) + (color(blue)(-3/5) xx color(red)(5))`

`y - color(red)(1) = -3/5x + (color(blue)(-3/cancel(5)) xx color(red)(cancel(5)))`

`y - color(red)(1) = -3/5x - 3`

`y - color(red)(1) + 1 = -3/5x - 3 + 1`

`y - 0 = -3/5x - 2`

`y = color(red)(-3/5)x - color(blue)(2)`