Question

How do you find an equation of the line having the given slope and containing the given point m=-8, (4,5)?

Answer 1

Use the slope-point formula to complete this question. See full explanation below.

Explanation:

Because we have been given a slope and a point on the line we can use the point-slope formula to complete this problem.

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 information we are provided gives us this equation:

`(y - color(red)(5)) = color(blue)(-8)(x - color(red)(4))`

If we want to put this in the more familiar form of the slope-intercept form we can solve for `y` as follows:

`y - color(red)(5) = color(blue)(-8)x - (color(blue)(-8) xx color(red)(4)))`

`y - color(red)(5) = color(blue)(-8)x - (-32)`

`y - color(red)(5) = color(blue)(-8)x + 32`

`y - color(red)(5) + 5 = color(blue)(-8)x + 32 + 5`

`y - 0 = color(blue)(-8)x + 37`

`y = -8x + 37`