SOLUTION: find the coordinates of the point where the line 4y+6x+2=0 meets the line through PQ P=(3,5) Q=(-1,3) the equation is Y=1/2x+3.5 PLEASE HELP!!

Algebra ->  Linear-equations -> SOLUTION: find the coordinates of the point where the line 4y+6x+2=0 meets the line through PQ P=(3,5) Q=(-1,3) the equation is Y=1/2x+3.5 PLEASE HELP!!      Log On


   

Question 462176: find the coordinates of the point where the line 4y+6x+2=0 meets the line through PQ
P=(3,5)
Q=(-1,3)
the equation is Y=1/2x+3.5
PLEASE HELP!!
Answer by rwm(914) About Me  (Show Source):
You can put this solution on YOUR website!
First find the equation of the line PQ
Solved by pluggable solver: Finding the Equation of a Line
First lets find the slope through the points (-1,3) and (3,5)


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 (-1,3) and (x%5B2%5D,y%5B2%5D) is the second point (3,5))


m=%285-3%29%2F%283--1%29 Plug in y%5B2%5D=5,y%5B1%5D=3,x%5B2%5D=3,x%5B1%5D=-1 (these are the coordinates of given points)


m=+2%2F4 Subtract the terms in the numerator 5-3 to get 2. Subtract the terms in the denominator 3--1 to get 4




m=1%2F2 Reduce



So the slope is

m=1%2F2





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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-3=%281%2F2%29%28x--1%29 Plug in m=1%2F2, x%5B1%5D=-1, and y%5B1%5D=3 (these values are given)



y-3=%281%2F2%29%28x%2B1%29 Rewrite x--1 as x%2B1



y-3=%281%2F2%29x%2B%281%2F2%29%281%29 Distribute 1%2F2


y-3=%281%2F2%29x%2B1%2F2 Multiply 1%2F2 and 1 to get 1%2F2

y=%281%2F2%29x%2B1%2F2%2B3 Add 3 to both sides to isolate y


y=%281%2F2%29x%2B7%2F2 Combine like terms 1%2F2 and 3 to get 7%2F2 (note: if you need help with combining fractions, check out this solver)



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Answer:



So the equation of the line which goes through the points (-1,3) and (3,5) is:y=%281%2F2%29x%2B7%2F2


The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=1%2F2 and the y-intercept is b=7%2F2


Notice if we graph the equation y=%281%2F2%29x%2B7%2F2 and plot the points (-1,3) and (3,5), we get this: (note: if you need help with graphing, check out this solver)


Graph of y=%281%2F2%29x%2B7%2F2 through the points (-1,3) and (3,5)


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



so using y=.5*x+3.5
or y=x/2+7/2
4y+6x=-2
substitute
4*(x/2+7/2)+6x+2=0
2x+14+6x+2=0
8x+16=0
8x=-16
x=-2
y=x/2+7/2
y=-2*1/2+7/2
y=-1+7/2
y=-2/2+7/2
y=5/2
(-2,5/2)