Question

What is the equation in y=mx+b of the line through points (0,2) , (1,7)?

Answer 1

`y=5x+2`

Explanation:

Given the points `(0,2)` and `(1,7)`
the slope is
`color(white)("XXXX")` `m = (Delta y)/(Delta x) = (7-2)/(1-0) = 5`

For any point `(x,y)` (combined with `(0,2)`) on this line the slope is
`color(white)("XXXX")` `m = (Delta y)/(Delta x) = (y-2)/(x-0)`

So
`color(white)("XXXX")` `(y-2)/(x-0) = 5`
or
`color(white)("XXXX")` `y-2 = 5x`

In slope y-intercept form (`y=mx+b`) this becomes
`color(white)("XXXX")` `y=5x+2`