How do you write the equation of a line in point slope form and slope intercept form given points (-2, 6) (5, 1)?

May 16, 2015

Your point slope form formula is=
$y - {y}_{1} = m \left(x - {x}_{1}\right)$

Where $m$ is representing your slope.

You need to find your ${x}_{1} , {y}_{1} , {x}_{2}$ and ${y}_{2}$.
Your first point in the first bracket is ${x}_{1}$. Second point in the first bracket is your ${y}_{1}$. First point in the second bracket is ${x}_{2}$ and second point in the second bracket is your ${y}_{2}$.

So,
${x}_{1} = - 2$
${y}_{1} = 6$
${x}_{2} = 5$
${y}_{2} = 1$

You need to find the slope before you can put it into point slope form.

To find slope using points, the formula is=

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

So your slope is going to be=

$\frac{1 - 6}{5 - - 2} = - \frac{5}{7}$

Your slope is $- \frac{5}{7}$

Next step is to substitute points into your point slope formula.
This is going to be

$y - 6 = - \frac{5}{7} \left(x - - 2\right)$ *Two negatives become a positive

Your point slope formula is equaled to

$y - 6 = - \frac{5}{7} \left(x + 2\right)$

To find slope intercept form first you have to eliminate the bracket.
To do so multiply everything in the bracket by -5/7.
Your equation will look like this

$y - 6 = - \frac{5}{7} x - \frac{10}{7}$

Next you have to isolate your y variable. To do so, add 6 to both sides.

$y - 6 + 6 = - \frac{5}{7} x - \frac{10}{7} + 6$

This will leave you with your slope intercept form which is

$y = - \frac{5}{7} x - \frac{32}{7}$