How do you write and equation of the line when it goes through (6,-2) and (-3,1)?

Question

How do you write and equation of the line when it goes through (6,-2) and (-3,1)?

Answer 1

slope  = -2-1/ 6--3 = -3/ +9 = -1/3

so y=mx+b

when x=6 y= -2 m = -1/3

-2= -1/3 * 6 +b

-2 = -2 +b

0 = b

so y = -1x/3 +0

Answer 2

There are several ways to do this.  You can write an equation of a line in slope-intercept form which is y = mx + b where m is the slope and b is the y-intercept.  Since you aren't given the y-intercept in the problem you can also write an equation of a line in point-slope form which is y - y1 = m(x - x1) where m is the slope and (x1, y1) is a point on the line.  Since you have two points on the line, it is easier to use this form.

Start by finding the slope.  Remember that the slope m is given by rise over run, or if the line includes the points (x1, y1) and (x2, y2) then the equation is below

m = (y1 - y2)/(x1 - x2)

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

m = (-3)/(6 + 3)

m = -3/9

m = -1/3

So the equation is given by

y - y1 = m(x - x1)

y - (-2) = (-1/3)(x - 6)

y + 2 = -(1/3)(x - 6)

Solve for y if you like.

y = -(1/3)(x - 6) - 2

This is the equation of the line that goes through (6, -2) and (-3, 1).  You can always turn this into slope-intercept form by rewritting it in the form y = mx + b

y = -(1/3)(x - 6) - 2

y = -(1/3)x - (-6/3) - 2

y = -(1/3)x + 2 - 2

y = -(1/3)x

This is also the equation of the line that goes through (6, -2) and (-3, 1).  The two equations are the same line and the same solution only expressed differently.

Hope this helps you!