Question

What is the equation, in slope-intercept form, of the line that contains the points (-1, 8) and (4, 3)?

A. y = -x + 7
B. y = x - 7
C. y = x - 1
D. y = 7x - 1

Answer 1

A

Explanation:

The equation of a line in slope- intercept form is

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

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 1, 8) and (x₂, y₂ ) = (4, 3)

m =
`(3-8)/(4+1)` =
`(-5)/(5)` = - 1, thus

y = - x + c ← is the partial equation of the line

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

Using (4, 3), then

3 = - 4 + c ⇒ c = 3 + 4 = 7

y = - x + 7 → A

Answer 2

A. y = -x + 7

Explanation:

First, find the rate of change [slope]:

-y₁ + y₂\-x₁ + x₂ = m

`-(8 + 3)/(1 + 4) = -(5)/(5) = -1`

Now, plug the coordinates into the Slope-Intercept Formula instead of the Point-Slope Formula because you get it done alot faster. It does not matter which ordered pair you choose:

3 = -1[4] + b

-4

7 = b

`y = -x + 7`

__________________________________________________________

8 = -1[-1] + b

1

7 = b

`y = -x + 7`

** You see? I told you it did not matter which ordered pair you choose because you will always get the exact same result.

I am joyous to assist you anytime.