# How do I find the equation of a linear function that passes through (1, 7) and (2, 9)?

Sep 17, 2014

For this type of problem we have 3 distinct steps to follow.

1) Find the slope using the formula $m = \frac{\left({y}_{2} - {y}_{1}\right)}{\left({x}_{2} - {x}_{1}\right)}$

2) Find the y-intercept, $b$, by substituting in the slope , $m$, from STEP 1 and the $x$ and $y$ values from one of the points given in the slope intercept formula, $y = m x + b$

3) Substitute the slope, $m$, and the y-intercept, $b$, back into the slope intercept formula, $y = m x + b$.

STEP 1

${x}_{1} = 1$
${y}_{1} = 7$

${x}_{2} = 2$
${y}_{2} = 9$

$m = \frac{\left({y}_{2} - {y}_{1}\right)}{\left({x}_{2} - {x}_{1}\right)} = \frac{\left(9 - 7\right)}{\left(2 - 1\right)} = \frac{2}{1} = 2$

STEP 2

$y = m x + b$

I will use the $x$ and $y$ values from the point $\left(1 , 7\right)$

$7 = \left(2\right) \left(1\right) + b$
$7 = 2 + b$
$5 = b$

STEP 3

$y = m x + b$

$y = 2 x + 5 \leftarrow S O L U T I O N$