# What is the equation in point-slope form of the line given (4,6),(5,7)?

Mar 6, 2018

$m = 1$

#### Explanation:

Given -

(4, 6); (5, 7)

${x}_{1} = 4$
${y}_{1} = 6$
${x}_{2} = 5$
${y}_{2} = 7$

$m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}} = \frac{7 - 6}{5 - 4} = \frac{1}{1} = 1$

$m = 1$

$y - 6 = 1 \left(x - 4\right)$

or

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

#### Explanation:

Point slope form is essentially:

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

${y}_{1}$ and ${x}_{1}$ are coordinates given to you. They can either be 6 and 4 respectively, or 7 and 5 respectively. Pick your choice.

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

So, plug in coordinates for that.

$\frac{7 - 6}{5 - 4} = \frac{1}{1} = 1 = m$

Remember, the plain ol' y and x in the point slope form equation will be the actual variables, since functions need those guys to stick around.