SOLUTION: Write the equation of the line (-3,4);(6,1)

Algebra ->  Linear-equations -> SOLUTION: Write the equation of the line (-3,4);(6,1)       Log On


   

Question 1205474: Write the equation of the line
(-3,4);(6,1)
Found 2 solutions by MathLover1, greenestamps:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

the equation of the line:
y=mx%2Bb
given points:

(-3,4)
(6,1)
find a slope:
m=%281-4%29%2F%286-%28-3%29%29=-3%2F9=-1%2F3
use point slope formula:
y-y1=m%28x-x1%29.....plug in a slope and the coordinates of one point
y-1=-%281%2F3%29%28x-6%29
y-1=-%281%2F3%29x%2B2
y=-%281%2F3%29x%2B2%2B1
y=-%281%2F3%29x%2B3




Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The question should read "Write AN equation for the line". There are many equivalent forms for the equation of any line.

One common form is slope-intercept form: y=mx%2Bb; m is the slope and b is the y-intercept.

To determine the slope for this problem, in your mind or on paper observe that the second point is 9 units to the right and 3 units down from the first point; the slope is "rise over run" = -3/9 = -1/3. So the slope-intercept form of the equation is of the form y=%28-1%2F3%29x%2Bb

Then one way to determine the y-intercept b is to plug the coordinates of either given point into that equation. Choosing the second point,

y=%28-1%2F3%29x%2Bb
1=%28-1%2F3%29%286%29%2Bb
1=-2%2Bb
b=3

So the slope-intercept form of the equation is

ANSWER: y=%28-1%2F3%29x%2B3