Question

A line passes through the points (8, –1) and (–4, 2). A coordinate plane. What is the y-intercept of this line?

-4
-1
1
4

Answer 1

y- intercept = 1

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 ) = (8, - 1) and (x₂, y₂ ) = (- 4, 2)

m =
`(2+1)/(-4-8)` =
`(3)/(-12)` = -
`(1)/(4)`, thus

y = -
`(1)/(4)` x + c ← is the partial equation

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

Using (8, - 1), then

- 1 = - 2 + c ⇒ - 1 + 2 = 1 ← y- intercept

Answer 2

y-intercept is 1

Explanation:

We need to find the equation of the line first.

Gradient

The gradient is found using the formula:

`m=(y_(2)-y_(1) )/(x_(2)-x_(1) )`

`m=(-1-2)/(8--4)`

`m=-(1)/(4)`

So the equation is y =
`-(1)/(4)`x + c

Finding c

To find c we need to substitute the value of x and y into the equation:

-1 =
`-(8)/(4)` + c

-1 = -2 + c

1 = c

And c is the y-intercept so it is 1