Question

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

Answer 1

The equation is y = -`2/3`x + `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 = `(7 - 1)/(-4 -5)` = `6/ -9` = -`2/3`

Substitute m into y = mx + c giving
y = -`2/3`x + c

to find c, substitute one of the given points into the above
So using (5, 1)
1 = -`2/3xx5` + c
1 = -`10/3` + c
c = 1 + `10/3` = `13/3`
It is best to keep the values as fractions, so the slope intercept form of the equation is
y = -`2/3`x + `13/3`