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

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) (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 which goes through the point (,), you can simply use the point-slope formula to find the equation:

---Point-Slope Formula---
where is the slope, and

is the given point

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

Plug in , , and (these values are given)

Distribute

Multiply and to get

Add 4 to both sides to isolate y

Combine like terms and to get
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Answer:

So the equation of the line with a slope of which goes through the point (,) is:

which is now in form where the slope is and the y-intercept is

Notice if we graph the equation and plot the point (,), we get (note: if you need help with graphing, check out this solver )

Graph of through the point (,)
and we can see that the point lies on the line. Since we know the equation has a slope of and goes through the point (,), this verifies our answer.

# 2

Start with the given equation.

Add 24 to both sides.

Notice we have a quadratic equation in the form of where , , and

Let's use the quadratic formula to solve for y

Start with the quadratic formula

Plug in , , and

Negate to get .

Square to get .

Multiply to get

Subtract from to get

Multiply and to get .

Take the square root of to get .

or Break up the expression.

or Combine like terms.

or Simplify.

So the answers are or

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