Question

Which of the following is the equation of a line that passes through (-2,1) and (-4,-3)?

Answer 1

Points
`X(-2,1)` and
`(-4,-3)` are defined therefore we have all data we need to construct equation.

Linear function has a form of,

`y=ax+b`

First calculate the slope a.

`a=(dy)/(dx)=(-3-1)/(-4-1)=(-4)/(-5)=(4)/(5)`

Now plug in the coordinates of either one of the points into the linear function. I'll pick point X.

`y=ax+b\Longrightarrow1=(4)/(5)\cdot(-2)+b`

Now just solve for b.

`1=-(8)/(5)+b\Longrightarrow b=(13)/(5)`

The equation is therefore,

`\boxed{y=(4)/(5)x+(13)/(5)}`

Hope this helps.

r3t40