Let
A(−6, 7) and B(10, −5)
be points in the plane.
(a) Find the slope of the line that contains A and B.
−
3
4

(b) Find an equation of the line that passes through A and B.

What are the intercepts?
x-intercept (x, y) =

y-intercept (x, y) =

(c) Find the midpoint of the segment AB.
(x, y) =

(d) Find the length of the segment AB.

(e) Find an equation of the perpendicular bisector of AB.

(f) Find an equation of the circle for which AB is a diameter.

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step-by-step explanatio89

i believe the answer is c.

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form