Question

Indicate the equation of the given line in standard form. The line with slope 9/7 and containing the midpoint of the segment whose endpoints are (2, -3) and (-6, 5).

Answer 1

The equation of the line in standard form is 9x - 7y = 87. To find the equation, we first need to find the midpoint of the segment. Using the midpoint and the slope, we can write the equation in point-slope form and then convert it to standard form.

Step-by-step explanation:

The equation of the line in standard form is 9x - 7y = 87.

To find the equation, we first need to find the midpoint of the segment. The midpoint formula is

M(x,y) = ((x1 + x2)/2, (y1 + y2)/2)

. Plugging in the coordinates of the endpoints, we get

M(x,y) = ((2 + (-6))/2, (-3 + 5)/2) = (-2, 1)

. Now, we have the midpoint and the slope. Using the point-slope form of a line

y - y1 = m(x - x1)

, we substitute

m = 9/7

and

(-2, 1)

for

(x1, y1)

. Solving for

y

, we get

y = (9/7)x + (5/7)

. Multiplying through by 7, we obtain

7y = 9x + 5

, and rearranging the terms, the line is in standard form as

9x - 7y = 87

Answer 2

I got y = 9/7x - 3/7