How do you write the equation in point slope form given ( 1/2 , -1 ) , ( -2/3 , 6 )?

1 Answer
Jun 30, 2017

y+1=-6(x-1/2)y+1=6(x12)

Explanation:

First, you need to know what the point-slope form of a line is. That is usually expressed as

y-y_1=m(x-x_1)yy1=m(xx1)

This form of the equation of a line is the final goal. We need to find both the slope, mm, and the point the line passes through at (x_1,y_1)(x1,y1).

To find the slope, mm, you need to have the slope formula.

m=(y_2-y_1)/(x_2-x_1)m=y2y1x2x1

Plugging in the points you were given, we get

m=(6-(-1))/((-2/3)-1/2)m=6(1)(23)12

m=(6+1)/(-4/6-3/6)m=6+14636

m=(7)/(-7/6)m=776

m=7xx(-6/7)=-6m=7×(67)=6

The first point you were given was (1/2,-1)(12,1), so you can plug this in for (x_1,y_1)(x1,y1) in the point-slope equation above.

y-y_1=m(x-x_1)yy1=m(xx1)

y-(-1)=-6(x-1/2)y(1)=6(x12)

y+1=-6(x-1/2)y+1=6(x12)