Question

(2, 1), (0, -7)
Write an equation of the line that passes through the given points

Answer 1

y = 4x - 7

Explanation:

The equation of a line in slope- intercept form is

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

Calculate m using the slope formula

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

with (x₁, y₁ ) = (2, 1) and (x₂, y₂ ) = (0, - 7)

m =
`(-7-1)/(0-2)` =
`(-8)/(-2)` = 4

The line crosses the y- axis at (0, - 7) ⇒ c = - 7

y = 4x - 7 ← equation of line

Answer 2

y=4x-7

Explanation:

We know that the y intercept is -7 so we can have y=mx-7

And we can get the slope by using the slope formula (y2-y1)/(x2-x1)=m

(2,1) (0,-7)

x1 y1 x2 y2

(-7-1)/(0-2)

-8/-2 = 4

m=4

So just plug it into the equation to get:

y=4x-7