Question

Write an equation if the line that passes through (0,-2) and (2,2)

Answer 1

`y=2x-2`

Explanation:

Hi there!

Linear equations are typically organized in slope-intercept form:
`y=mx+b` where m is the slope and b is the y-intercept (the value of y when the line crosses the y-axis)

1) Determine the slope (m)

`m=(y_2-y_1)/(x_2-x_1)` where the two points are
`(x_1,y_1)` and
`(x_2,y_2)`

Plug in the given points (0,-2) and (2,2)

`=(2-(-2))/(2-0)\\=(2+2)/(2)\\=(4)/(2)\\=2`

Therefore, the slope of the line is 2. Plug this into
`y=mx+b` as m:

`y=2x+b`

2) Determine the y-intercept (b)

`y=2x+b`

Plug in one of the given points and solve for b

`2=2(2)+b\\2=4+b`

Subtract 4 from both sides to isolate b

`2-4=4+b-4\\-2=b`

Therefore, the y-intercept of the line is -2. Plug this back into
`y=2x+b`

`y=2x-2`

I hope this helps!