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aniked [119]
3 years ago
15

Line $1$ represents the graph of $3x + 4y = -14$. Line $2$ passes through the point $(-5,7)$, and is perpendicular to line $1$.

If line $2$ represents the graph of $y=mx +b$, then find $m+b$.
Mathematics
1 answer:
Sophie [7]3 years ago
8 0

Answer:

15

Step-by-step explanation:

First, solve for Line 1

3x + 4y = -14

<em>move the x to the right of the equation</em>

4y = -3x - 14

<em>divide the whole equation by 4 </em>

y = -3/4x - 14/4

<u>Line 1 is y = -3/4x - 7/2 </u>

Then, solve for Line 2

Since Line 2 is perpendicular, change the sign of the slope of Line 1 and then get the reciprocal of that.

-3/4 to 3/4 to 4/3

4/3 is the slope of Line 2.

Now, we want to find what the b of the equation is, so we can plug in our x (-5) and our y (7) into the y=mx+b equation to find b. The 4/3 is the m or the slope.

y = mx + b

<em>plug in the y, m, and x into the equation</em>

7 = (4/3)(-5) + b

<em>multiply the m and x together </em>

7 = -20/3 + b

<em>add 20/3 to both sides so it will cancel out on the right of the equation and be added to the 7 on the left of the equation</em>

<u>41/3 = b </u>

So, m = 4/3 and b = 41/3

Add them together and you get 45/3 or 15.

I hope this helped!

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