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Line l_1 represents the graph of 3x + 4y = -14. Line l_2 passes through the point (-5,7), and is perpendicular to line l_1. If line l_2 represents the graph of y=mx +b, then find m+b.

 Jun 18, 2021

Best Answer 

 #1
avatar+48 
+2

Answer: 

 

44/3

 

Solution:

 

Hi Guest! Sorry for the late help 

 

Let's get  \(\mathrm{Line_1}\) into standard form first, yeah?

\(\mathrm{Line_1}\) = 

 

3x+4y=-14

      4y=-3x-14

       y=-3x/4 -7/2

 

So now that \(\mathrm{Line_1}\) is now happily in standard form, let's start looking for \(\mathrm{Line_2}\)'s equation.

 

First, let's find the slope.

 

To find a perpendicular line, you have to take the opposite reciprocal of \(\mathrm{Line_1}\)'s slope, which is -3/4.

 

So \(\mathrm{Line_2}\)'s new slope is 4/3. 

 

What we have so far for \(\mathrm{Line_2}\): y=4/3 x + b

 

Now we need to find b.

 

We can do that by plugging in (-5,7), a point on the line, into x and y in the partially done equation for  \(\mathrm{Line_2}\).

 

y = 4/3 x + b <-- before plugging in

7 = 4/3 * -5 + b <-- after plugging in

7 = -20/3 + b <-- simplifying

41/3 = b <-- even more simplifying

b = 41/3 <-- just flipping it nothing here to see

 

So we have the full equation for \(\mathrm{Line_2}\), or, y = 4/3 x + 41/3.

 

From here, we look at the question again. What is it asking for?

 

"find m+b"

m = 4/3, and b= 41/3. 

 

Hence, the answer is 44/3.

 

=^-^=

If you find a mistake, please let me know in the replies!

 Jun 18, 2021
 #1
avatar+48 
+2
Best Answer

Answer: 

 

44/3

 

Solution:

 

Hi Guest! Sorry for the late help 

 

Let's get  \(\mathrm{Line_1}\) into standard form first, yeah?

\(\mathrm{Line_1}\) = 

 

3x+4y=-14

      4y=-3x-14

       y=-3x/4 -7/2

 

So now that \(\mathrm{Line_1}\) is now happily in standard form, let's start looking for \(\mathrm{Line_2}\)'s equation.

 

First, let's find the slope.

 

To find a perpendicular line, you have to take the opposite reciprocal of \(\mathrm{Line_1}\)'s slope, which is -3/4.

 

So \(\mathrm{Line_2}\)'s new slope is 4/3. 

 

What we have so far for \(\mathrm{Line_2}\): y=4/3 x + b

 

Now we need to find b.

 

We can do that by plugging in (-5,7), a point on the line, into x and y in the partially done equation for  \(\mathrm{Line_2}\).

 

y = 4/3 x + b <-- before plugging in

7 = 4/3 * -5 + b <-- after plugging in

7 = -20/3 + b <-- simplifying

41/3 = b <-- even more simplifying

b = 41/3 <-- just flipping it nothing here to see

 

So we have the full equation for \(\mathrm{Line_2}\), or, y = 4/3 x + 41/3.

 

From here, we look at the question again. What is it asking for?

 

"find m+b"

m = 4/3, and b= 41/3. 

 

Hence, the answer is 44/3.

 

=^-^=

If you find a mistake, please let me know in the replies!

TheOddOne Jun 18, 2021

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