SOLUTION: 10.) find the slope of the line that passes thru (6,-2) and (-3,2) 11.) find the equation of a line that passes thru the points (-11,-4) and (9,8) 12.) Rewrite the equation y

Algebra ->  Graphs -> SOLUTION: 10.) find the slope of the line that passes thru (6,-2) and (-3,2) 11.) find the equation of a line that passes thru the points (-11,-4) and (9,8) 12.) Rewrite the equation y      Log On


   

Question 941857: 10.) find the slope of the line that passes thru (6,-2) and (-3,2)
11.) find the equation of a line that passes thru the points (-11,-4) and (9,8)
12.) Rewrite the equation y=3x-7 in function notation and find f(8)
13.) Determine whether the graphs of 2x+3y=6 and 6y=-4x+7 are parallel, perpendicular, or neither.
Found 2 solutions by MathLover1, Alan3354:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
10.) find the slope of the line that passes thru (6,-2) and (-3,2)
Solved by pluggable solver: Finding the Equation of a Line
First lets find the slope through the points (6,-2) and (-3,2)


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 (6,-2) and (x%5B2%5D,y%5B2%5D) is the second point (-3,2))


m=%282--2%29%2F%28-3-6%29 Plug in y%5B2%5D=2,y%5B1%5D=-2,x%5B2%5D=-3,x%5B1%5D=6 (these are the coordinates of given points)


m=+4%2F-9 Subtract the terms in the numerator 2--2 to get 4. Subtract the terms in the denominator -3-6 to get -9




m=-4%2F9 Reduce



So the slope is

m=-4%2F9





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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=%28-4%2F9%29%28x-6%29 Plug in m=-4%2F9, x%5B1%5D=6, and y%5B1%5D=-2 (these values are given)



y%2B2=%28-4%2F9%29%28x-6%29 Rewrite y--2 as y%2B2



y%2B2=%28-4%2F9%29x%2B%28-4%2F9%29%28-6%29 Distribute -4%2F9


y%2B2=%28-4%2F9%29x%2B8%2F3 Multiply -4%2F9 and -6 to get 24%2F9. Now reduce 24%2F9 to get 8%2F3

y=%28-4%2F9%29x%2B8%2F3-2 Subtract 2 from both sides to isolate y


y=%28-4%2F9%29x%2B2%2F3 Combine like terms 8%2F3 and -2 to get 2%2F3 (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 (6,-2) and (-3,2) is:y=%28-4%2F9%29x%2B2%2F3


The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=-4%2F9 and the y-intercept is b=2%2F3


Notice if we graph the equation y=%28-4%2F9%29x%2B2%2F3 and plot the points (6,-2) and (-3,2), we get this: (note: if you need help with graphing, check out this solver)


Graph of y=%28-4%2F9%29x%2B2%2F3 through the points (6,-2) and (-3,2)


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





11.) find the equation of a line that passes thru the points (-11,-4) and (9,8)
Solved by pluggable solver: Finding the Equation of a Line
First lets find the slope through the points (-11,-4) and (9,8)


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 (-11,-4) and (x%5B2%5D,y%5B2%5D) is the second point (9,8))


m=%288--4%29%2F%289--11%29 Plug in y%5B2%5D=8,y%5B1%5D=-4,x%5B2%5D=9,x%5B1%5D=-11 (these are the coordinates of given points)


m=+12%2F20 Subtract the terms in the numerator 8--4 to get 12. Subtract the terms in the denominator 9--11 to get 20




m=3%2F5 Reduce



So the slope is

m=3%2F5





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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--4=%283%2F5%29%28x--11%29 Plug in m=3%2F5, x%5B1%5D=-11, and y%5B1%5D=-4 (these values are given)



y%2B4=%283%2F5%29%28x--11%29 Rewrite y--4 as y%2B4



y%2B4=%283%2F5%29%28x%2B11%29 Rewrite x--11 as x%2B11



y%2B4=%283%2F5%29x%2B%283%2F5%29%2811%29 Distribute 3%2F5


y%2B4=%283%2F5%29x%2B33%2F5 Multiply 3%2F5 and 11 to get 33%2F5

y=%283%2F5%29x%2B33%2F5-4 Subtract 4 from both sides to isolate y


y=%283%2F5%29x%2B13%2F5 Combine like terms 33%2F5 and -4 to get 13%2F5 (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 (-11,-4) and (9,8) is:y=%283%2F5%29x%2B13%2F5


The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=3%2F5 and the y-intercept is b=13%2F5


Notice if we graph the equation y=%283%2F5%29x%2B13%2F5 and plot the points (-11,-4) and (9,8), we get this: (note: if you need help with graphing, check out this solver)


Graph of y=%283%2F5%29x%2B13%2F5 through the points (-11,-4) and (9,8)


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






since you can't see the points on a graph above, I will do it again:




12.) Rewrite the equation y=3x-7 in function notation and find f%288%29
f%28x%29=3x-7
f%288%29=3%2A8-7
f%288%29=24-7
f%288%29=17

13.) Determine whether the graphs of 2x%2B3y=6 and 6y=-4x%2B7 are parallel, perpendicular, or neither.
parallel lines have same slope
perpendicular lines have slopes negative reciprocal to each other
let's find the slopes; write both equations in slope-intercept form y=mx%2Bb where m is a slope and b is y-intercept
2x%2B3y=6
6y=-4x%2B7
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3y=-2x%2B6
6y=-4x%2B7
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y=-%282%2F3%29x%2B2
y=-%28cross%284%292%2Fcross%286%293%29x%2B7%2F6
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y=highlight%28-%282%2F3%29%29x%2B2
y=highlight%28-%282%2F3%29%29x%2B7%2F6
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as you can see, both lines have same slope which means they are parallel lines
see them on a graph:


Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!

11.) find the equation of a line that passes thru the points (-11,-4) and (9,8)
Find the slope, m
m = diffy/diffx = (-2-2)/(6 +3) = -4/9
Then y - y1 = m*(x - x1) where (x1,y1) is either point.
y - 8 = (-4/9)*(x - 9)
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10.) find the slope of the line that passes thru (6,-2) and (-3,2)
Do it like #11
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12.) Rewrite the equation y=3x-7 in function notation and find f(8)
f(x) = 3x-7
---
Sub 8 for x
f(8) = 3*8-7
f(8) = 17
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13.) Determine whether the graphs of 2x+3y=6 and 6y=-4x+7 are parallel, perpendicular, or neither.
Change the eqns to slope-intercept form y = mx + b
That means solve for y.
2x+3y=6
3y = -2x + 6
y = (-2/3)x + 2
m = -2/3
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If the slope m of the other equation is equal, they're parallel.
If it's the negative inverse ( = 3/2) they're perpendicular.
o/w neither.