SOLUTION: Please Help! I have five questions I been working on and I am at a stand still. First Question Find an equation of the line having the given slope and containing the given point. m

Algebra ->  Linear-equations -> SOLUTION: Please Help! I have five questions I been working on and I am at a stand still. First Question Find an equation of the line having the given slope and containing the given point. m      Log On


   

Question 171849: Please Help! I have five questions I been working on and I am at a stand still. First Question Find an equation of the line having the given slope and containing the given point. m=3(3,2) The equation of the line is y=? (simplify your answer. Use inters or fractions for any number of expression.


The second problem. write an equation of the line containing the given point and perendicular to the given line. (6,7):2x+y=4 The equation of the line is y=?


The third write an equation of the line containing the given point and perpenicular to the given line (7,-8):8x+7y=3 The equation of the line is y=? (type in the form y=mx+b. simplify your answer. type an integer or fraction.


Fourth question Find the equation of the line having the given slope and containing the given point m=3,(3,2)


and fifth question write an equation of the line containing the given point and parallel to the given line. Expressyour answer in the form y=mx+b. (-9,7);5x=7y+9 The equation of the line is y=? Simplify your answer. use integers or fractions for any number in the expression.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Note: I don't mean to be nitpicky, but please use spaces between your problems (as it's hard to find where one problem ends and another begins).

# 1


If you want to find the equation of line with a given a slope of 3 which goes through the point (3,2), 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-2=%283%29%28x-3%29 Plug in m=3, x%5B1%5D=3, and y%5B1%5D=2 (these values are given)


y-2=3x%2B%283%29%28-3%29 Distribute 3

y-2=3x-9 Multiply 3 and -3 to get -9

y=3x-9%2B2 Add 2 to both sides to isolate y

y=3x-7 Combine like terms -9 and 2 to get -7
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Answer:


So the equation of the line with a slope of 3 which goes through the point (3,2) is:

y=3x-7 which is now in y=mx%2Bb form where the slope is m=3 and the y-intercept is b=-7

Notice if we graph the equation y=3x-7 and plot the point (3,2), we get (note: if you need help with graphing, check out this solver)

Graph of y=3x-7 through the point (3,2)
and we can see that the point lies on the line. Since we know the equation has a slope of 3 and goes through the point (3,2), this verifies our answer.





# 2


2x%2By=4 Start with the given equation.


y=4-2x Subtract 2x from both sides.


y=-2x%2B4 Rearrange the terms.


We can see that the equation y=-2%2Ax%2B4 has a slope m=-2 and a y-intercept b=4.


Now to find the slope of the perpendicular line, simply flip the slope m=-2 to get m=-1%2F2. Now change the sign to get m=1%2F2. So the perpendicular slope is m=1%2F2.


Now let's use the point slope formula to find the equation of the perpendicular line by plugging in the slope m=-2 and the coordinates of the given point .


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


y-7=%281%2F2%29%28x-6%29 Plug in m=1%2F2, x%5B1%5D=6, and y%5B1%5D=7


y-7=%281%2F2%29x%2B%281%2F2%29%28-6%29 Distribute


y-7=%281%2F2%29x-3 Multiply


y=%281%2F2%29x-3%2B7 Add 7 to both sides.


y=%281%2F2%29x%2B4 Combine like terms.


So the equation of the line perpendicular to 2x%2By=4 that goes through the point is y=%281%2F2%29x%2B4.


Here's a graph to visually verify our answer:
Graph of the original equation y=-2%2Ax%2B4 (red) and the perpendicular line y=%281%2F2%29x%2B4 (green) through the point .






# 3


8x%2B7y=3 Start with the given equation.


7y=3-8x Subtract 8x from both sides.


7y=-8x%2B3 Rearrange the terms.


y=%28-8x%2B3%29%2F%287%29 Divide both sides by 7 to isolate y.


y=%28%28-8%29%2F%287%29%29x%2B%283%29%2F%287%29 Break up the fraction.


y=-%288%2F7%29x%2B3%2F7 Reduce.


We can see that the equation y=-%288%2F7%29x%2B3%2F7 has a slope m=-8%2F7 and a y-intercept b=3%2F7.


Now to find the slope of the perpendicular line, simply flip the slope m=-8%2F7 to get m=-7%2F8. Now change the sign to get m=7%2F8. So the perpendicular slope is m=7%2F8.


Now let's use the point slope formula to find the equation of the perpendicular line by plugging in the slope m=-8%2F7 and the coordinates of the given point .


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


y--8=%287%2F8%29%28x-7%29 Plug in m=7%2F8, x%5B1%5D=7, and y%5B1%5D=-8


y%2B8=%287%2F8%29%28x-7%29 Rewrite y--8 as y%2B8


y%2B8=%287%2F8%29x%2B%287%2F8%29%28-7%29 Distribute


y%2B8=%287%2F8%29x-49%2F8 Multiply


y=%287%2F8%29x-49%2F8-8 Subtract 8 from both sides.


y=%287%2F8%29x-113%2F8 Combine like terms. note: If you need help with fractions, check out this solver.


So the equation of the line perpendicular to 8x%2B7y=3 that goes through the point is y=%287%2F8%29x-113%2F8.


Here's a graph to visually verify our answer:
Graph of the original equation y=-%288%2F7%29x%2B3%2F7 (red) and the perpendicular line y=%287%2F8%29x-113%2F8 (green) through the point .




# 4

This problem is identical to the first question. Make sure that you've entered everything correctly




# 5


5x=7y%2B9 Start with the given equation.


5x-9=7y Subract 9 from both sides.


%285x-9%29%2F7=y Divide both sides by 7 to isolate y.


y=%285x-9%29%2F7 Rearrange the equation.


y=%285%2F7%29x-9%2F7 Break up the fraction.



We can see that the equation y=%285%2F7%29x-9%2F7 has a slope m=5%2F7 and a y-intercept b=-9%2F7.


Since parallel lines have equal slopes, this means that we know that the slope of the unknown parallel line is m=5%2F7.


Now let's use the point slope formula to find the equation of the parallel line by plugging in the slope m=5%2F7 and the coordinates of the given point .


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


y-7=%285%2F7%29%28x--9%29 Plug in m=5%2F7, x%5B1%5D=-9, and y%5B1%5D=7


y-7=%285%2F7%29%28x%2B9%29 Rewrite x--9 as x%2B9


y-7=%285%2F7%29x%2B%285%2F7%29%289%29 Distribute


y-7=%285%2F7%29x%2B45%2F7 Multiply


y=%285%2F7%29x%2B45%2F7%2B7 Add 7 to both sides.


y=%285%2F7%29x%2B94%2F7 Combine like terms. note: If you need help with fractions, check out this solver.


So the equation of the line parallel to 5x=7y%2B9 that goes through the point is y=%285%2F7%29x%2B94%2F7.


Here's a graph to visually verify our answer:
Graph of the original equation 5x=7y%2B9 (red) and the parallel line y=%285%2F7%29x%2B94%2F7 (green) through the point .