SOLUTION: Find the value of r so the line that passes through each pair of points has the given slope the the question is (4,-5),(r,3) m=8

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Question 791325: Find the value of r so the line that passes through each pair of points has the given slope the the question is (4,-5),(r,3) m=8
Found 2 solutions by solver91311, MathLover1:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Use the slope formula:



where and are the coordinates of the given points.

Plug in the values you know, replace the remaining variable with and then solve for

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Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

use the "point-slope" formula:
y+-y1+=+m%28x-x1%29
given:
(4,-5),(r,3) and m=8
y-y1+=+m%28x+-x1%29....plug in (x=4,y=-5) and m=8
y-%28-5%29+=+8%28x+-4%29
y+%2B5=+8%28x-4%29
y+=+8x-32-5
highlight%28y+=+8x+-37%29.....eq.1

y+-y1+=+m%28x-+x1%29....plug in (x=r,y=3) and m=8
y-3+=+8%28x-r%29
y+%2B3=+8x+%96+8r
y+=+8x+-8r-3.....eq.2
since in both eq.1 and eq.2, left sides are equal, make right sides equal too

+8x+-37=8x+-8r-3
+cross%288x%29+-37=cross%288x%29+-8r-3
-37=+-8r-3
-37%2B37=+-8r%2B37-3
8r=+-8r%2B8r%2B34
8r=34
r=34%2F8
r=4.25
so, other point is (4.25,3) and equation of a line is
y+=+8x+-8%2A4.25%2B3.....eq.2
y+=+8x+-34%2B3
highlight%28y+=+8x+-31%29.....eq.2
the line that passes through each pair of points will be:

Solved by pluggable solver: FIND a line by slope and one point

What we know about the line whose equation we are trying to find out:

  • it goes through point (4, -5)

  • it has a slope of 8



First, let's draw a diagram of the coordinate system with point (4, -5) plotted with a little blue dot:



Write this down: the formula for the equation, given point x%5B1%5D%2C+y%5B1%5D and intercept a, is

y=ax+%2B+%28y%5B1%5D-a%2Ax%5B1%5D%29 (see a paragraph below explaining why this formula is correct)

Given that a=8, and system%28+x%5B1%5D+=+4%2C+y%5B1%5D+=+-5+%29+, we have the equation of the line:

y=8%2Ax+%2B+-37

Explanation: Why did we use formula y=ax+%2B+%28y%5B1%5D+-+a%2Ax%5B1%5D%29 ? Explanation goes here. We are trying to find equation y=ax+b. The value of slope (a) is already given to us. We need to find b. If a point (x%5B1%5D, y%5B1%5D) lies on the line, it means that it satisfies the equation of the line. So, our equation holds for (x%5B1%5D, y%5B1%5D): y%5B1%5D+=+a%2Ax%5B1%5D%2Bb Here, we know a, x%5B1%5D, and y%5B1%5D, and do not know b. It is easy to find out: b=y%5B1%5D-a%2Ax%5B1%5D. So, then, the equation of the line is: +y=ax%2B%28y%5B1%5D-a%2Ax%5B1%5D%29+.

Here's the graph:





Solved by pluggable solver: FIND a line by slope and one point

What we know about the line whose equation we are trying to find out:

  • it goes through point (4.25, 3)

  • it has a slope of 8



First, let's draw a diagram of the coordinate system with point (4.25, 3) plotted with a little blue dot:



Write this down: the formula for the equation, given point x%5B1%5D%2C+y%5B1%5D and intercept a, is

y=ax+%2B+%28y%5B1%5D-a%2Ax%5B1%5D%29 (see a paragraph below explaining why this formula is correct)

Given that a=8, and system%28+x%5B1%5D+=+4.25%2C+y%5B1%5D+=+3+%29+, we have the equation of the line:

y=8%2Ax+%2B+-31

Explanation: Why did we use formula y=ax+%2B+%28y%5B1%5D+-+a%2Ax%5B1%5D%29 ? Explanation goes here. We are trying to find equation y=ax+b. The value of slope (a) is already given to us. We need to find b. If a point (x%5B1%5D, y%5B1%5D) lies on the line, it means that it satisfies the equation of the line. So, our equation holds for (x%5B1%5D, y%5B1%5D): y%5B1%5D+=+a%2Ax%5B1%5D%2Bb Here, we know a, x%5B1%5D, and y%5B1%5D, and do not know b. It is easy to find out: b=y%5B1%5D-a%2Ax%5B1%5D. So, then, the equation of the line is: +y=ax%2B%28y%5B1%5D-a%2Ax%5B1%5D%29+.

Here's the graph:





as you can see, both lines have a slope 8