Question

- the line through (3, 7) and (-1, 4) --

Answer 1

`y = (3)/(4)x + (19)/(4)`

Explanation:

We have to get the equation of the straight line through the points (3,7) and (-1,4).

Now, we know that the two-point formula of a straight line passing through the two points
`(x_(1),y_(1))` and
`(x_(2),y_(2))` is given by

`(y - y_(1) )/(y_(1) - y_(2)) = (x - x_(1) )/(x_(1) - x_(2))`.

So, in our case, the equation of the straight line will be

`(y - 7)/(7 - 4) = (x - 3)/(3 + 1)`

⇒ 4(y - 7) = 3(x - 3)

⇒ 4y - 28 = 3x - 9

⇒ 4y = 3x + 19

⇒
`y = (3)/(4)x + (19)/(4)` (Answer)