Question

Write the equation of the line in fully simplified slope-intercept form.

Answer 1

`y = -(2)/(5) x-6`

Explanation:

1) First, find the slope of the line. Use the slope formula
`m =(y_2-y_1)/(x_2-x_1)`. Pick two points on the line and substitute their x and y values into the formula, then solve. I used the points (-5,-4) and (0,-6):

`m = ((-6)-(-4))/((0)-(-5)) \\m = (-6+4)/(0+5) \\m = (-2)/(5) \\`

So, the slope of the line is
`-(2)/(5)`.

2) Next, use the point-slope formula
`y-y_1 = m (x-x_1)` to write the equation of the line in point-slope form. (From there, we can convert it to slope-intercept form.) Substitute values for the
`m`,
`x_1` and
`y_1` into the formula.

Since
`m` represents the slope, substitute
`-(2)/(5)` in its place. Since
`x_1` and
`y_1` represent the x and y values of one point on the line, pick any point on the line (any one is fine, it will equal the same thing at the end) and substitute its x and y values in those places. (I chose (0,-6), as seen below.) Then, with the resulting equation, isolate y to put the equation in slope-intercept form:

`y-(-6) = -(2)/(5) (x-(0))\\y + 6 = -(2)/(5) x\\y = -(2)/(5) x-6`