Question

What is an equation of the line that passes through the points (0, -7) and (-8, 3)?

Answer 1

Answer (assuming it can be in slope-intercept form):

`y = -(5)/(4) x-7`

Explanation:

1) First, find the slope of the line by using the slope formula,
`m = (y_2-y_1)/(x_2-x_1)`. Substitute the x and y values of the given points into the formula and solve:

`m = ((3)-(-7))/((-8)-(0))\\m = (3+7)/(-8-0) \\m = (10)/(-8) \\m = -(5)/(4)`

So, the slope is
`-(5)/(4)`.

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

Since
`m` represents the slope, substitute
`-(5)/(4)` in its place. Since
`x_1` and
`y_1` represent the x and y values of one point the line intersects, choose any one of the given points (either one is fine, it will equal the same thing at the end) and substitute its x and y values into the formula as well. (I chose (0, -7), as seen below.) Then, isolate y to put the equation in slope-intercept form and find the following answer:

`y-(-7) = -(5)/(4) (x-(0))\\y + 7 = -(5)/(4) x\\y = -(5)/(4) x-7`