Question

What is the equation of the line passing through `(11,13)` and `(59,67)`?

Answer 1

`y=1.125x + 0.625`
or
`y=9/8 x + 5/8`

Explanation:

First label the coordinates.
`x1 = 11, y1 =13`
`x2 = 59, y2 = 67`

The slope (m) is the rise (change in y) divided by the run (change in x),
so `m = (y2 - y1)/(x2-x1)`

`m = (67-13)/(59-11) = 54/48 = 9/8 = 1.125`

The standard linear formula is `y=mx+b` and we have to find b. Substitute m and one set of coordinates into this formula:

`y1=m*x1+b-> 13 = 1.125 * 11 + b -> 13 = 12.375 +b`

`b=0.625`

Substitute this into `y=mx+b -> **y = 1.125 x + 0.625**`

Always check your answer by substituting the other set of coordinates into the equation:

`y = 1.125 * **59** +0.625 = 66.375 + 0.625 = 67`

Since this matches the original coordinate (59, 67), the answer must be correct.