# How do you write an equation in slope intercept form given (5, 1) and (-4, 7)?

Mar 19, 2016

The equation is y = -$\frac{2}{3}$x + $\frac{13}{3}$

#### Explanation:

The slope intercept form is y = mx +c
where m is the slope and c is the intercept
To find m, find the difference between the y values divided by the difference between the corresponding x values of the two points
The points are (5, 1) and (-4, 7)
so
m = $\frac{7 - 1}{- 4 - 5}$ = $\frac{6}{-} 9$ = -$\frac{2}{3}$

Substitute m into y = mx + c giving
y = -$\frac{2}{3}$x + c

to find c, substitute one of the given points into the above
So using (5, 1)
1 = -$\frac{2}{3} \times 5$ + c
1 = -$\frac{10}{3}$ + c
c = 1 + $\frac{10}{3}$ = $\frac{13}{3}$
It is best to keep the values as fractions, so the slope intercept form of the equation is
y = -$\frac{2}{3}$x + $\frac{13}{3}$