SOLUTION: I need to find an equation of the line containing the given pair of points; (-3,-1) and (-9,-6). The equation of the line in the slope-intercept is y=? m=y2-y1= -6-(-1)= -5 x

Algebra ->  Linear-equations -> SOLUTION: I need to find an equation of the line containing the given pair of points; (-3,-1) and (-9,-6). The equation of the line in the slope-intercept is y=? m=y2-y1= -6-(-1)= -5 x      Log On


   

Question 274720: I need to find an equation of the line containing the given pair of points; (-3,-1) and (-9,-6). The equation of the line in the slope-intercept is y=?
m=y2-y1= -6-(-1)= -5
x2-x1 -9-(-3) -6
y-(-1)=m(x-x1)
y-(-1)=-5(x-(-3))
-6
y-(-1)=-5x-5
-6 2
y=-5 -3
6x 2
Apparently I did this wrong somewhere and I am not sure what I did wrong. Can someone help me please.
Found 3 solutions by jim_thompson5910, edjones, stanbon:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

First let's find the slope of the line through the points and


Note: is the first point . So this means that x%5B1%5D=-3 and y%5B1%5D=-1.
Also, is the second point . So this means that x%5B2%5D=-9 and y%5B2%5D=-6.


m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula.


m=%28-6--1%29%2F%28-9--3%29 Plug in y%5B2%5D=-6, y%5B1%5D=-1, x%5B2%5D=-9, and x%5B1%5D=-3


m=%28-5%29%2F%28-9--3%29 Subtract -1 from -6 to get -5


m=%28-5%29%2F%28-6%29 Subtract -3 from -9 to get -6


m=5%2F6 Reduce


So the slope of the line that goes through the points and is m=5%2F6


Now let's use the point slope formula:


y-y%5B1%5D=m%28x-x%5B1%5D%29 Start with the point slope formula


y--1=%285%2F6%29%28x--3%29 Plug in m=5%2F6, x%5B1%5D=-3, and y%5B1%5D=-1


y--1=%285%2F6%29%28x%2B3%29 Rewrite x--3 as x%2B3


y%2B1=%285%2F6%29%28x%2B3%29 Rewrite y--1 as y%2B1


y%2B1=%285%2F6%29x%2B%285%2F6%29%283%29 Distribute


y%2B1=%285%2F6%29x%2B5%2F2 Multiply


y=%285%2F6%29x%2B5%2F2-1 Subtract 1 from both sides.


y=%285%2F6%29x%2B3%2F2 Combine like terms. note: If you need help with fractions, check out this solver.


So the equation that goes through the points and is y=%285%2F6%29x%2B3%2F2

Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
(-3,-1) and (-9,-6)
m=(-1-(-6))/-3-(-9) The Y's on top; X's in denominator.
=5/6
.
y-(-1)=5/6 (x-(-3)) Point-slope form
y+1=5/6 (x+3)
y+1=5x/6 + 15/6
y=5x/6 + 9/6
y=5x/6 + 3/2 Slope intercept form
.
Ed

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
I need to find an equation of the line containing the given pair of points;
(-3,-1) and (-9,-6).
The equation of the line in the slope-intercept is y= mx + b
-------------------
To get the equation you only need to determine "m" and "b";
---
m= (-6--1)/(-9--3) = -5/-6 = 5/6
---------------------------------
Now solve for "b":
You know m = 5/6 and you know y=-1 when x = -3:
Using the form y = mx+b, solve for "b:
-1 = (5/6)(-3) + b
-1 = -5/2 + b
b = -1 + (5/2)
b = 3/2
-----------------
Write the equation:
y = (5/6)x + (3/2)
=========================
Cheers,
Stan H.