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Help would be greatly appreciated

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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

#1
+2

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.

=^-^=

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

Jun 18, 2021

#1
+2

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.