Question

Find the equation of the line
Use exact numbers

Answer 1

The answer is y = x - 5

Sub in 0 to find the y intercept, and count rise over run to find the slope (1)

Answer 2

y = 1x + -5

Explanation:

slope-intercept form is y = mx + b, where m = slope and b = y-intercept.

the line touches the y-axis at -5, therefore the y-intercept, or b, is -5.

y = mx + b ⇒ y = mx - 5

now i'll find the slope by picking two points from the line and finding the change in y over the change in x, aka
`(y_2-y_1)/(x_2-x_1)`. i'll use the points (8, 3) and (5, 0) from the line in order to calculate the slope. (8, 3) can be my
`x_2` and
`y_2` and (5, 0) can be my
`x_1` and
`y_1`.

first, i'm going to plug in my
`y_2` and
`y_1` values, which are the y-values from each of the coordinate pairs. since i picked (8, 3) for
`x_2` and
`y_2` and (5, 0) for
`x_1` and
`y_1`, i will be plugging in 3 for
`y_2` and 0 for
`y_1`.

`(y_2-y_1)/(x_2-x_1)` ⇒
`(3-0)/(x_2-x_1)`

then i'll plug in my
`x_2` and
`x_1` values, which will be 8 and 5.

`(3-0)/(x_2-x_1)` ⇒
`(3-0)/(8-5)`

now simplify by subtracting 0 from 3 and 5 from 8.

• 3 - 0 = 3

• 8 - 5 = 3

the slope is
`(3)/(3)`, which simplifies to 1 because
`(3)/(3)` or 3 ÷ 3 = 1.

the slope-intercept form equation for this line is y = 1x + -5 (or just y = x - 5, but since it's a fill-in-the-blank problem, the 1 will show in front of the y and -5 will come after the + sign.)

i hope this helps! have a lovely day <3