Question

Which of the following are point-slope equations of the line going through

(-4,-7) and (3, 2)? Check all that apply.
PLEASSSEEE HELP I’VE BEEN STUCK ON THIS FOR A COUPLE OF DAYS .. 15 points

Answer 1

The equations of the line are

y + 7 =
`(9)/(7)` (x + 4) ⇒ B

y - 2 =
`(9)/(7)` (x - 3) ⇒ E

Explanation:

The point-slope form of the linear equation is

`y-y1=m(x-x1)` , where

• m is the slope of the line

• (x1, y1) is a point on the line

• The rule of the slope is
  `m=(y2-y1)/(x2-x1)`

∵ The line passes through points (-4, -7) and (3, 2)

∴ x1 = -4 and y1 = -7

∴ x2 = 3 and y2 = 2

→ Use the rule of the slope above to find it

∵
`m=(2--7)/(3--4)=(2+7)/(3+4)=(9)/(7)`

∴ The slope of the line is
`(9)/(7)`

→ Substitute the values of m and (x1, y1) in the form of the equation above

∵ y - -7 =
`(9)/(7)` (x - -4)

∴ y + 7 =
`(9)/(7)` (x + 4)

∴ The equation of the line is y + 7 =
`(9)/(7)` (x + 4)

→ Substitute the values of m and (x2, y2) in the form of the equation above

∵ y - 2 =
`(9)/(7)` (x - 3)

∴ The equation of the line is y - 2 =
`(9)/(7)` (x - 3)

→ Look at the answers to find the same equations

∴ Answers B and E have the same equations