# What is the point-slope form of the line that passes through (4,6),(5,7)?

Mar 9, 2018

$y - 6 = x - 4$

#### Explanation:

Point - slope form of equation is $y - {y}_{1} = m \left(x - {x}_{1}\right)$

Given $\left({x}_{1} = 4 , {y}_{1} = 6 , {x}_{2} = 5 , {y}_{2} = 7\right)$

We know two points. Now we have to find the slope “m”.

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

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

Hence point - slope form of equation is $y - 6 = 1 \cdot \left(x - 4\right)$

$y - 6 = x - 4$ or $y - 7 = x - 5$ both the equations are same.

graph{x + 2 [-10, 10, -5, 5]}