# How do I write an equation in slope intercept form, standard form, and point-slope form using two points (2,-5) and (7,12)?

Apr 3, 2015

First you find the slope, which is the amount $y$ changes for every increase of $x$

Slope-intercept is of the form $y = m x + b$

Slope= $\text{change in y"/"change in x}$ or more formally:

$m = \frac{\Delta y}{\Delta x} = \frac{12 - \left(- 5\right)}{7 - 2} = \frac{17}{5} = 3 \frac{2}{5} \mathmr{and} 3.4$

Now you know the slope, fill in what you know for one of the points:

$y = m x + b \to - 5 = 3 \frac{2}{5} \cdot 2 + b \to b = - 11 \frac{4}{5} \mathmr{and} 11.8$

So the whole equation goes: $y = 3 \frac{2}{5} x - 11 \frac{4}{5} \to y = 3.4 x - 11.8$

Check with the other point:

$3.4 \cdot 7 - 11.8 = 12$ --check!