Question

What is the equation of the line with slope `m= 14/25` that passes through `(23/5, (-23)/10)`?

Answer 1

`y = (14x)/25 + 4 219/250`

This is a somewhat unrealistic question, and becomes an exercise in arithmetic rather than maths.

Explanation:

There are 2 methods:

Method 1 . uses the formula `(y - y_1) = m(x - x_1)`
This is great to use if you know the slope (m) and one point, which is exactly what we have here. It involves one step of substitution and a bit of simplifying.

`(y - y_1) = m(x - x_1)`

`(y - (-23/10)) = 14/25(x - 23/5)`

`y + 23/10 = (14x)/25 - 14/25 xx23/5 " " xx250`

`250y + 250xx23/10 = 250xx(14x)/25 - 250xx14/25 xx23/5`

`250y + 575 = 140x - 28 xx23`

`250y = 140x + 1219`

`y = (14x)/25 + 4 219/250`

Method 2 uses `y = mx + c`

Subst for `m, x and y` to find `c`

`(-23/10) = 14/25 xx 23/5 + c " " xx 250`

`250xx(-23/10) = 250xx14/25 xx 23/5 + 250c`

`-575 = 644 + 250c`

`1219 = 250c`

`c = 1219/250 = 4 219/250`

This leads to the same equation, using values for m and c.

`y = (14x)/25 + 4 219/250`.