SOLUTION: Anyone able to figure this one out? Thanks for your assistance. What is the equation of the line through points (-3, 2) and (-4, 5)? a. y= (-3/2)-7 b. y= -3x-7 c. y= -3x+7

Algebra ->  Linear-equations -> SOLUTION: Anyone able to figure this one out? Thanks for your assistance. What is the equation of the line through points (-3, 2) and (-4, 5)? a. y= (-3/2)-7 b. y= -3x-7 c. y= -3x+7      Log On


   

Question 91140: Anyone able to figure this one out? Thanks for your assistance.
What is the equation of the line through points (-3, 2) and (-4, 5)?
a. y= (-3/2)-7
b. y= -3x-7
c. y= -3x+7
Found 2 solutions by checkley71, jim_thompson5910:
Answer by checkley71(8403) About Me  (Show Source):
You can put this solution on YOUR website!
slope=(5-2)/(-4+3)=3/-1=-3.
now supstitute one set of coordinates in the line equation with a slope of -3 & solve for the y intercept(b)
2=-3*-3+b
2=9+b
b=2-9
b=-7 thus the equation is
y=-3x-7 or answer B).

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Finding the Equation of a Line
First lets find the slope through the points (-3,2) and (-4,5)


m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula (note: (x%5B1%5D,y%5B1%5D) is the first point (-3,2) and (x%5B2%5D,y%5B2%5D) is the second point (-4,5))


m=%285-2%29%2F%28-4--3%29 Plug in y%5B2%5D=5,y%5B1%5D=2,x%5B2%5D=-4,x%5B1%5D=-3 (these are the coordinates of given points)


m=+3%2F-1 Subtract the terms in the numerator 5-2 to get 3. Subtract the terms in the denominator -4--3 to get -1




m=-3 Reduce



So the slope is

m=-3





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Now let's use the point-slope formula to find the equation of the line:




------Point-Slope Formula------
y-y%5B1%5D=m%28x-x%5B1%5D%29 where m is the slope, and (x%5B1%5D,y%5B1%5D) is one of the given points


So lets use the Point-Slope Formula to find the equation of the line


y-2=%28-3%29%28x--3%29 Plug in m=-3, x%5B1%5D=-3, and y%5B1%5D=2 (these values are given)



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



y-2=-3x%2B%28-3%29%283%29 Distribute -3


y-2=-3x-9 Multiply -3 and 3 to get -9%2F1. Now reduce -9%2F1 to get -9

y=-3x-9%2B2 Add 2 to both sides to isolate y


y=-3x-7 Combine like terms -9 and 2 to get -7

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Answer:



So the equation of the line which goes through the points (-3,2) and (-4,5) is:y=-3x-7


The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=-3 and the y-intercept is b=-7


Notice if we graph the equation y=-3x-7 and plot the points (-3,2) and (-4,5), we get this: (note: if you need help with graphing, check out this solver)


Graph of y=-3x-7 through the points (-3,2) and (-4,5)


Notice how the two points lie on the line. This graphically verifies our answer.