SOLUTION: Find the equation of the line that contains the points (-1,-2) and (-3,0) A. y=-x-3 B. y=x+3 C. y=1/2x-3/2 D. y=1/2x+3/2

Algebra ->  Linear-equations -> SOLUTION: Find the equation of the line that contains the points (-1,-2) and (-3,0) A. y=-x-3 B. y=x+3 C. y=1/2x-3/2 D. y=1/2x+3/2      Log On


   

Question 169806: Find the equation of the line that contains the points (-1,-2) and (-3,0)
A. y=-x-3
B. y=x+3
C. y=1/2x-3/2
D. y=1/2x+3/2
Found 2 solutions by jim_thompson5910, jojo14344:
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


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


m=%280--2%29%2F%28-3--1%29 Plug in y%5B2%5D=0, y%5B1%5D=-2, x%5B2%5D=-3, and x%5B1%5D=-1


m=%282%29%2F%28-3--1%29 Subtract -2 from 0 to get 2


m=%282%29%2F%28-2%29 Subtract -1 from -3 to get -2


m=-1 Reduce


So the slope of the line that goes through the points and is m=-1


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


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


y%2B2=-1%28x%2B1%29 Rewrite y--2 as y%2B2


y%2B2=-1x%2B-1%281%29 Distribute


y%2B2=-1x-1 Multiply


y=-1x-1-2 Subtract 2 from both sides.


y=-1x-3 Combine like terms.


y=-x-3 Simplify


So the equation that goes through the points and is y=-x-3


Notice how the graph of y=-x-3 goes through the points and . So this visually verifies our answer.
Graph of y=-x-3 through the points and

Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!
Given: (-1,-2) and (-3,0)
We get the Slope=m,
Via Point-Slope Form: m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29
Subst. m=%280-%28-2%29%29%2F%28-3-%28-1%29%29=%280%2B2%29%2F%28-3%2B1%29
m=-2%2F2=-1
.
Thru points (-1,-2):
Via Slope-intercept form: y=mx%2Bb
-1=%28-1%29%28-2%29%2Bb
-1=2%2Bb
b=-1-2=-3
.
Thru points (-3,0), should be the same:
0=%28-1%29%28-3%29%2Bb
b-3=0 ---> b=-3
f(y)=0:
0=-1x-3
-x=3 ----> x=-3
So then, via Slope Intercept form:
highlight%28y=-x-3%29, Answer (A)
See below,

Thank you,
Jojo