Question

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

Answer 1

Answer:

y-intercept is 1

Step-by-step explanation:

We need to find the equation of the line first.

Gradient

The gradient is found using the formula:

$m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }$

$m=\frac{-1-2}{8--4}$

$m=-\frac{1}{4}$

So the equation is y = $-\frac{1}{4}$x + c

Finding c

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

-1 = $-\frac{8}{4}$ + c

-1 = -2 + c

1 = c

And c is the y-intercept so it is 1

Answer 2

Answer:

y- intercept = 1

Step-by-step 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 = $\frac{2+1}{-4-8}$ = $\frac{3}{-12}$ = - $\frac{1}{4}$, thus

y = - $\frac{1}{4}$ 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