Question

How do you write the equation that passes through the given points (8,0) and (0,-4)

Answer 1

Our answer is: y = 1/2x - 4.

`\Large\texttt{Explanation}`

We are asked to write an equation for the line that passes through the following points -

(8,0) and (0,-4)

First, we're going to find the slope using the formula:

`\sf{m=\cfrac{y_2-y_1}{x_2-x_1}}`

Substitute the values:

`\sf{m=\cfrac{-4-0}{0-8}}`

`\sf{m=\cfrac{-4}{-8}}`

`\sf{m=\cfrac{4}{8}}`

`\sf{m=\cfrac{1}{2}}`

So far, our equation is:
`\sf{y=\cfrac{1}{2}x}`.

We also need the y-intercept. And to find that, look at the second point, which is (0,-4). Since its x-coordinate is 0, we can use the y-coordinate as the y-intercept:

`\boxed{\sf{y=\cfrac{1}{2}x-4}}`

`\therefore` y = 1/2x - 4 is the equation.

`\rule{300}{5}`

Answer 2

y =
`(1)/(2)` x - 4

Explanation:

the equation of a line in slope- intercept form is

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

calculate slope m, using the slope formula

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

let (x₁, y₁ ) = (8, 0 ) and (x₂, y₂ ) = (0, - 4 )

substitute these values into the formula for m

m =
`(-4-0)/(0-8)` =
`(-4)/(-8)` =
`(1)/(2)`

the line crosses the y- axis at (0, - 4 ) , then c = - 4

y =
`(1)/(2)` x - 4 ← equation of line