SOLUTION: 1. find the slope and y intercept of the line -2x+3y=3. 2. find the equation of the line that passes through the points(-3,-4)and (0,5). 3. Find the equation of the line that

Question 174259: 1. find the slope and y intercept of the line -2x+3y=3.
2. find the equation of the line that passes through the points(-3,-4)and (0,5).
3. Find the equation of the line that contains the point (-4,19) and has slope -5.

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
# 1

Start with the given equation.

Add to both sides.

Rearrange the terms.

Divide both sides by to isolate y.

Break up the fraction.

Reduce.

So the equation is now in slope intercept form where the slope is and the y-intercept is note: the y-intercept is the point

# 2

First let's find the slope of the line through the points

and

Start with the slope formula.

Plug in , , , and

Subtract from to get

Subtract from to get

Reduce

So the slope of the line that goes through the points

and

is

Now let's use the point slope formula:

Start with the point slope formula

Plug in , , and

Rewrite as

Rewrite as

Distribute

Multiply

Subtract 4 from both sides.

Combine like terms.

Simplify

So the equation that goes through the points

and

is

Notice how the graph of goes through the points

and

. So this visually verifies our answer.
Graph of through the points

and

# 3

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)

Rewrite as

Distribute

Multiply and to get

Add 19 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.
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