Question

Give the POINT SLOPE equation of the line
that contains:
f(-1) = -7 and f(3) = -6.

Answer 1

Point-Slope Form

This is one way we can represent a linear equation:

`y-y_1=m(x-x_1)`

• 
  `(x_1,y_1)` is a point that falls on the line
• 
  `m` is the slope

Solving the Question

We're given:

• Line contains
  `f(-1) = -7` and
  `f(3) = -6`

These functions give us information on two points, as they are represented as
`f(x)=y`:

• 
  `f(-1) = -7` ⇒ (-1, -7)
• 
  `f(3) = -6` ⇒ (3,-6)

First, solve for the slope:

`m=(y_2-y_1)/(x_2-x_1)`

⇒ Plug in the two points:

`m=(-6-(-7))/(3-(-1))\\\\m=(-6+7)/(3+1)\\\\m=(1)/(4)`

⇒ Plug this into
`y_2-y_1=m(x_2-x_1)`:

`y-y_1=(1)/(4)(x-x_1)`

Now, there are two ways we can write this equation, as we are given two points:

(-1, -7)

⇒
`y-(-7)=(1)/(4)(x-(-1))\\y+7=(1)/(4)(x+1)`

(3,-6)

⇒
`y-(-6)=(1)/(4)(x-(3))\\y+6=(1)/(4)(x-3)`

Answer

`y+7=(1)/(4)(x+1)` or
`y+6=(1)/(4)(x-3)`