Question

Write an equation
of the line in slope - Intercept form
(8,3) (0,-5)

Answer 1

y=x-5

Explanation:

Hi there!

We want to write an equation of the line that passes through the points (8,3) and (0,-5) in slope-intercept form

Slope-intercept form is given as y=mx+b, where m is the slope, and b is the y intercept

So let's first find the slope of the line

The formula for the slope calculated from two points is
`(y_2-y_1)/(x_2-x_1)`, where
`(x_1, y_1)` and
`(x_2, y_2)` are points

We have everything needed to find the slope, but let's label the values of the points to avoid any confusion

`x_1=8\\y_1=3\\x_2=0\\y_2=-5`

Now substitute into the formula

m=
`(y_2-y_1)/(x_2-x_1)`

m=
`(-5-3)/(0-8)`

Subtract

m=
`(-8)/(-8)`

Simplify

m=1

The slope is 1

Here is the equation of the line so far:

y=1x+b (can also be written as y=x+b)

We need to find b

The equation passes through both (8, 3) and (0, -5), so we can substitute the values of either one of them as x and y to solve for b

Let's take (8, 3) for example

Substitute 8 as x and 3 as y

3=1(8)+b

Multiply

3=8+b

Subtract 8 from both sides

-5=b

Substitute -5 as b into the equation

y=x-5

Hope this helps!