# What is the equation of the line passing through (31,32) and (1,2)?

Jun 18, 2016

$y - 32 = 1 \left(x - 31\right)$

#### Explanation:

$S l o p e = \frac{31 - 1}{32 - 2} = 1$

$y - 32 = 1 \left(x - 31\right)$

Jun 20, 2016

$y = x + 1$

#### Explanation:

There is a VERY useful formula for finding the equation of a straight line if we are given two points on the line.

It is quicker and easier than any other method I know and involves substituting ONCE, then some simplifying.

The formula is based on the fact that a straight line has a constant slope.

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

Call the two points $\left({x}_{1} , {y}_{1}\right) \mathmr{and} \left({x}_{2} , {y}_{2}\right)$.
I will use B(1,2) as $\left({x}_{1} , {y}_{1}\right)$ and A(31,32) as $\left({x}_{2} , {y}_{2}\right)$

Do not substitute for $x \mathmr{and} y$ - they are the $x \mathmr{and} y$ in the equation $y = m x + c$

$\frac{y - 2}{x - 1} = \frac{32 - 2}{31 - 1} = \frac{30}{30} = \frac{1}{1} \text{ simplify the fraction}$

$\frac{y - 2}{x - 1} = \frac{1}{1} \text{ now cross-multiply}$

$y - 2 = x - 1 \text{ multiply out and change to standard form}$

$y = x - 1 + 2$

$y = x + 1$