SOLUTION: Hello I am having trouble in finding slope and intercept forms and I need help on some problems: 1. Find the slope and y-intercept of y-6= -2x AND y= x+2 Also, 1. Find the s

Algebra ->  Graphs -> SOLUTION: Hello I am having trouble in finding slope and intercept forms and I need help on some problems: 1. Find the slope and y-intercept of y-6= -2x AND y= x+2 Also, 1. Find the s      Log On


   

Question 102158: Hello I am having trouble in finding slope and intercept forms and I need help on some problems:
1. Find the slope and y-intercept of y-6= -2x AND y= x+2
Also,
1. Find the slope of the line that passes through each pair of points:
(-3,-2),(4,-2)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
"Find the slope and y-intercept of y-6= -2x"
y-6=+-2x+ Start with the given equation


y=+-2x%2B6+ Add 6 to both sides. So the equation is in slope intercept form y=mx%2Bb where the slope is m=-2 and the y-intercept is b=6


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"Find the slope and y-intercept of y= x+2"

Since y=+x%2B2+ is in slope intercept form y=mx%2Bb, the slope is m=1 (remember it really looks like y=1%2Ax%2B2) and the y-intercept is b=2



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"Find the slope of the line that passes through each pair of points:
(-3,-2),(4,-2)"
Solved by pluggable solver: Finding the Equation of a Line
First lets find the slope through the points (-3,-2) and (4,-2)


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,-2))


m=%28-2--2%29%2F%284--3%29 Plug in y%5B2%5D=-2,y%5B1%5D=-2,x%5B2%5D=4,x%5B1%5D=-3 (these are the coordinates of given points)


m=+0%2F7 Subtract the terms in the numerator -2--2 to get 0. Subtract the terms in the denominator 4--3 to get 7




m=0 Reduce



So the slope is

m=0





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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=%280%29%28x--3%29 Plug in m=0, x%5B1%5D=-3, and y%5B1%5D=-2 (these values are given)



y%2B2=%280%29%28x--3%29 Rewrite y--2 as y%2B2



y%2B2=%280%29%28x%2B3%29 Rewrite x--3 as x%2B3



y%2B2=0x%2B%280%29%283%29 Distribute 0


y%2B2=0x%2B0 Multiply 0 and 3 to get 0%2F0. Now reduce 0%2F0 to get 0

y=0x%2B0-2 Subtract 2 from both sides to isolate y


y=0x-2 Combine like terms 0 and -2 to get -2

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Answer:



So the equation of the line which goes through the points (-3,-2) and (4,-2) is:y=0x-2


The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=0 and the y-intercept is b=-2


Notice if we graph the equation y=0x-2 and plot the points (-3,-2) and (4,-2), we get this: (note: if you need help with graphing, check out this solver)


Graph of y=0x-2 through the points (-3,-2) and (4,-2)


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





So y=0x-2 then becomes y=-2, which is the equation of the line through the points (-3,-2),(4,-2)