How do you write an equation given points (5,7), (6,8)?

1 Answer
Nov 13, 2016

$y = x + 2$

Explanation:

First, find the slope of the line using slope formula:

$m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$

Where $m$ is the slope

$\left(5 , 7\right) \implies \left({x}_{1} , {y}_{1}\right)$

$\left(6 , 8\right) \implies \left({x}_{2} , {y}_{2}\right)$

$m = \frac{8 - 7}{6 - 5} = \frac{1}{1} = 1$

Next, pick a set of coordinate points and plug them into point slope form:

$y - {y}_{1} = m \left(x - {x}_{1}\right)$

And the slope of $1$

If you use $\left(5 , 7\right)$:

$y - 7 = 1 \left(x - 5\right)$

Distribute the one throughout the set of parenthesis

$y - 7 = x - 5$

Add $7$ on both sides of the equation

$y = x + 2$

If you were to use the other set of coordinate points, the equation should be the same:

If you use $\left(6 , 8\right)$:

$y - 8 = 1 \left(x - 6\right)$

Distribute the one throughout the set of parenthesis

$y - 8 = x - 6$

Add $8$ on both sides of the equation

$y = x + 2$