Question

Question and choices are in the photo please explain the answer

Answer 1

A

Explanation:

For this question, you want to use y=mx+c, where m is the gradient and c is the y-intercept.

We can see the line passes through (-4, 6) and (-1,2), so we can use those points to work out the gradient.

The formula for gradient is m=
`(y_(2) -y_(1))/(x_(2)-x_(1))`. By substituting the values above, you get m=
`(6-2)/(-4--1)`, which becomes
`(4)/(-3)` or
`-(4)/(3)`.

Since we can't exactly determine the y-intercept from the photo, we can sub it in to what we already know to work it out.

Using the point (-4, 6), y=
`-(4)/(3)`x+c can be written as 6=
`-(4)/(3)`(-4)+c.

This can be expanded to 6=
`(16)/(3)`+c or 6=
`5(1)/(3)`+c.

Subtracting
`-(4)/(3)` from both sides gives c=
`(2)/(3)`.

Putting this all back in the question, we get y=
`-(4)/(3)`x+
`-(4)/(3)`, or A.

**This question involves writing linear equations, which you may want to revise. I'm always happy to help!