How do you write an equation of a line given (3, 5) and (-6, -1)?

1 Answer
Aug 14, 2017

Find the gradient and the y-intercept in y = mx + c to get

3y = 2x + 9

Explanation:

y=mx+c is the slope-intercept equation of any straight line. So we need to find m, the gradient of the line, and c, the y-intercept.

m = ( y_2 - y_1 ) / ( x_2 - x_1 )

y_2 being the second y value, which is -1, and y_1 is 5. The same goes for x_2 and x_1, so

m = ( -1 - 5 ) / (-6-3)

m = (-6)/-9 = 2/3

Since

y = mx+c

to find c do

c = y - mx

We substitute one of the coordinates, for eg. ( 3 , 5 ), so

c = 5 - (2/3)*3

c = 3

Therefore, we substitute the values of m and c in y = mx + c
to get

y = 2/3x+3

3y = 2x + 9