Question

Indicate the equation of the given line in standard form. The line with slope and containing the midpoint of the segment whose endpoints are (2, -3) and (-6, 5).

Answer 1

x + y = -1

Explanation:

To write the equation of a line, find the slope and use it with a point in the point slope form.

You can find the slope using the slope formula.

`m = (y_2-y_1)/(x_2-x_1) = (5--3)/(-6-2) = (8)/(-8)=-1`

Substitute m = -1 and the point (2,-3) into the point slope form.

`y - y_1 = m(x-x_1)\\y --3 = -1(x-2)\\y+3=-1(x-2)`

Convert to standard form by applying the distributive property and rearranging the terms.

y+3 = -1(x-2)

y + 3 = -x + 2

x + y + 3 = 2

x + y = -1