Question

Which linear equation passes through the points (0, - 2) and (4, 10)?

y = 3x - 2

y = - 1/3x - 2

y = 1/3x - 2

y = - 3x - 2

Answer 1

y = 3x - 2

Explanation:

You can easily find the equation of a line through two points by using the point-slope form,
`y-y_1=m(x-x_1)`, where m is the slope and
`(x_1,y_1)` is one of the points.

First, let's find the slope of the line through (0, -2) and (4, 10).

`m=\displaystyle (y_2-y_1)/(x_2-x_1) = (10-(-2))/(4-0)=(12)/(4)=3`

Next, we plug this into point-slope form. Remember that we let (0, -2) be our first point,
`(x_1,y_1)`.

`y-(-2)=3(x-0)`

Finally, we rearrange this equation to get the slope-intercept form
`y=mx+b`, where b is the y-intercept.

`y+2=3x \\ y=3x-2`

We can verify using the attached graph that both points lie on this line.

Answer 2

Y=-1/3x-2 is the answer