Question

Write an equation in slope-intercept form of the line that passes through (-1, 4) and (0, 2).

y =

Answer 1

`y=-2x+2`

Explanation:

Hi there!

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

Plug in the given points (-1, 4) and (0, 2)

`=(2-4)/(0-(-1))\\=(-2)/(0+1)\\=(-2)/(1)\\= -2`

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

`y=-2x+b`

2) Determine the y-intercept

`y=-2x+b`

Recall that the y-intercept is the value of y when the line crosses the y-axis, meaning that the y-intercept occurs when x is equal to 0.

One of the given points is (0,2). Notice how y=2 when x=0. Therefore, the y-intercept of the line is 2.

Plug this back into the equation:

`y=-2x+2`

I hope this helps!