SOLUTION: 1. find the equation of the line that has a slope of -3/4 and y intercept (0,4). 2.solve: y^2-11y=-24 3. graph by using the slope and y-intercept: y=2x-4

Algebra ->  Linear-equations -> SOLUTION: 1. find the equation of the line that has a slope of -3/4 and y intercept (0,4). 2.solve: y^2-11y=-24 3. graph by using the slope and y-intercept: y=2x-4       Log On


   

Question 174264: 1. find the equation of the line that has a slope of -3/4 and y intercept (0,4).
2.solve: y^2-11y=-24
3. graph by using the slope and y-intercept: y=2x-4
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'll do the first two to get you going in the right direction

# 1



If you want to find the equation of line with a given a slope of -3%2F4 which goes through the point (0,4), you can simply use the point-slope formula to find the equation:


---Point-Slope Formula---
y-y%5B1%5D=m%28x-x%5B1%5D%29 where m is the slope, and is the given point

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

y-4=%28-3%2F4%29%28x-0%29 Plug in m=-3%2F4, x%5B1%5D=0, and y%5B1%5D=4 (these values are given)


y-4=%28-3%2F4%29x%2B%28-3%2F4%29%28-0%29 Distribute -3%2F4

y-4=%28-3%2F4%29x%2B0 Multiply -3%2F4 and -0 to get 0

y=%28-3%2F4%29x%2B0%2B4 Add 4 to both sides to isolate y

y=%28-3%2F4%29x%2B4 Combine like terms 0 and 4 to get 4
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Answer:


So the equation of the line with a slope of -3%2F4 which goes through the point (0,4) is:

y=%28-3%2F4%29x%2B4 which is now in y=mx%2Bb form where the slope is m=-3%2F4 and the y-intercept is b=4

Notice if we graph the equation y=%28-3%2F4%29x%2B4 and plot the point (0,4), we get (note: if you need help with graphing, check out this solver)

Graph of y=%28-3%2F4%29x%2B4 through the point (0,4)
and we can see that the point lies on the line. Since we know the equation has a slope of -3%2F4 and goes through the point (0,4), this verifies our answer.




# 2



y%5E2-11y=-24 Start with the given equation.


y%5E2-11y%2B24=0 Add 24 to both sides.


Notice we have a quadratic equation in the form of ay%5E2%2Bby%2Bc where a=1, b=-11, and c=24


Let's use the quadratic formula to solve for y


y+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


y+=+%28-%28-11%29+%2B-+sqrt%28+%28-11%29%5E2-4%281%29%2824%29+%29%29%2F%282%281%29%29 Plug in a=1, b=-11, and c=24


y+=+%2811+%2B-+sqrt%28+%28-11%29%5E2-4%281%29%2824%29+%29%29%2F%282%281%29%29 Negate -11 to get 11.


y+=+%2811+%2B-+sqrt%28+121-4%281%29%2824%29+%29%29%2F%282%281%29%29 Square -11 to get 121.


y+=+%2811+%2B-+sqrt%28+121-96+%29%29%2F%282%281%29%29 Multiply 4%281%29%2824%29 to get 96


y+=+%2811+%2B-+sqrt%28+25+%29%29%2F%282%281%29%29 Subtract 96 from 121 to get 25


y+=+%2811+%2B-+sqrt%28+25+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


y+=+%2811+%2B-+5%29%2F%282%29 Take the square root of 25 to get 5.


y+=+%2811+%2B+5%29%2F%282%29 or y+=+%2811+-+5%29%2F%282%29 Break up the expression.


y+=+%2816%29%2F%282%29 or y+=++%286%29%2F%282%29 Combine like terms.


y+=+8 or y+=+3 Simplify.


So the answers are y+=+8 or y+=+3