Question

Through: (-4,-1) and ( -1,2) ?

(A) y=-x+3.
(B)y=4x+3
(X) y=5x+3
(E)y=x+3
(D)y=3x+1

Answer 1

(E)
`y=x+3`

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=\displaystyle (y_2-y_1)/(x_2-x_1)` where two points that fall on the line are
`(x_1,y_1)` and
`(x_2,y_2)`

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

`m=\displaystyle (2-(-1))/((-1)-(-4))\\\\m=\displaystyle (2+1)/(-1+4)\\\\m=\displaystyle (3)/(3)\\\\m=1`

Therefore, the slope of the line is 1. Plug this into
`y=mx+b`:

`y=1x+b\\y=x+b`

2) Determine the y-intercept (b)

`y=x+b`

Plug in one of the given points and solve for b:

`2=-1+b\\2+1=b\\3=b`

Therefore, the y-intercept of the line is 3. Plug this back into the original equation:

`y=x+3`

I hope this helps!