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

Algebra ->  Linear-equations -> 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      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
# 1


-2x%2B3y=3 Start with the given equation.


3y=3%2B2x Add 2x to both sides.


3y=2x%2B3 Rearrange the terms.


y=%282x%2B3%29%2F%283%29 Divide both sides by 3 to isolate y.


y=%28%282%29%2F%283%29%29x%2B%283%29%2F%283%29 Break up the fraction.


y=%282%2F3%29x%2B1 Reduce.


So the equation y=%282%2F3%29x%2B1 is now in slope intercept form y=mx%2Bb where the slope is m=2%2F3 and the y-intercept is b=1 note: the y-intercept is the point






# 2




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


m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula.


m=%285--4%29%2F%280--3%29 Plug in y%5B2%5D=5, y%5B1%5D=-4, x%5B2%5D=0, and x%5B1%5D=-3


m=%289%29%2F%280--3%29 Subtract -4 from 5 to get 9


m=%289%29%2F%283%29 Subtract -3 from 0 to get 3


m=3 Reduce


So the slope of the line that goes through the points and is m=3


Now let's use the point slope formula:


y-y%5B1%5D=m%28x-x%5B1%5D%29 Start with the point slope formula


y--4=3%28x--3%29 Plug in m=3, x%5B1%5D=-3, and y%5B1%5D=-4


y--4=3%28x%2B3%29 Rewrite x--3 as x%2B3


y%2B4=3%28x%2B3%29 Rewrite y--4 as y%2B4


y%2B4=3x%2B3%283%29 Distribute


y%2B4=3x%2B9 Multiply


y=3x%2B9-4 Subtract 4 from both sides.


y=3x%2B5 Combine like terms.


y=3x%2B5 Simplify


So the equation that goes through the points and is y=3x%2B5


Notice how the graph of y=3x%2B5 goes through the points and . So this visually verifies our answer.
Graph of y=3x%2B5 through the points and





# 3




If you want to find the equation of line with a given a slope of -5 which goes through the point (-4,19), 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-19=%28-5%29%28x--4%29 Plug in m=-5, x%5B1%5D=-4, and y%5B1%5D=19 (these values are given)


y-19=%28-5%29%28x%2B4%29 Rewrite x--4 as x%2B4


y-19=-5x%2B%28-5%29%284%29 Distribute -5

y-19=-5x-20 Multiply -5 and 4 to get -20

y=-5x-20%2B19 Add 19 to both sides to isolate y

y=-5x-1 Combine like terms -20 and 19 to get -1
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Answer:


So the equation of the line with a slope of -5 which goes through the point (-4,19) is:

y=-5x-1 which is now in y=mx%2Bb form where the slope is m=-5 and the y-intercept is b=-1

Notice if we graph the equation y=-5x-1 and plot the point (-4,19), we get (note: if you need help with graphing, check out this solver)

Graph of y=-5x-1 through the point (-4,19)
and we can see that the point lies on the line. Since we know the equation has a slope of -5 and goes through the point (-4,19), this verifies our answer.