Question

Find the equation of the line between the points (10, – 5) and ( - 2,0).

Answer 1

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

`y = -(5)/(12) x-(5)/(6)`

Explanation:

1) First, find the slope of the line between the two points 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 = ((0)-(-5))/((-2)-(10)) \\m = (0+5)/(-2-10) \\m=(5)/(-12)`

Thus, the slope of the line is
`-(5)/(12)`.

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. Substitute values for
`m`,
`x_1`, and
`y_1` in the formula.

Since
`m` represents the slope, substitute
`-(5)/(12)` in its place. Since
`x_1` and
`y_1` represent the x and y values of one point the line intersects, choose any of the given points (it doesn't matter which one, it will equal the same thing) and substitute its x and y values into the formula as well. (I chose (-2,0), as seen below.) Then, isolate y and expand the right side in the resulting equation to find the equation of the line in slope-intercept form:

`y-(0)=-(5)/(12) (x-(-2))\\y-0 = -(5)/(12) (x+2)\\y = -(5)/(12) x-(5)/(6)`