Mathematics, 04.04.2020 04:14 shardonnay2160

The equation y=-7x-5 and another equation have a solution of (-2,9). what is the second equation?

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I'm guessing there's a menu of choices to go with this one, and we just need to try (-2,9) with each choice. But it's a much more interesting problem without the menu.

First we verify (-2,9) is on the line y=-7x-5,

-7(-2)-5 = 14-5 = 9, good.

There's a whole family of possibilities for the second equation, basically all the other lines through (-2,9). Believe it or not, that's called a pencil of lines. We need two parameters a and b, whose values only matter in ratio, to represent all these. If we tried to do it with just the slope we'd miss one line, the vertical line x=-2.

We'll do the line through (-2,9) and (a,b). A little thought tells us it's

(a + 2)(y - 9) = (b - 9)(x + 2)

When we plug in (-2,9) we get 0=0, good. When we plug in (a,b) we get

(a + 2)(b - 9) = (b - 9)(a + 2)

which is also true.

(a + 2)(y - 9) = (b - 9)(x + 2)

(b - 9)x - (a+2)y = -9(a + 2) - 2(b-9)

(b - 9)x - (a+2)y = -9a - 2b

We can choose any a and b and we'll get the line through (-2,9) and (a,b), so it will have a solution (-2,9) where it meets y = -7x - 5.

We need to make sure (a,b) isn't already on y = -7x - 5 which is the same line twice.

For arbitrary a,b, b ≠ -7a - 5, the lines y = -7x - 5 and

(b - 9)x - (a+2)y = -9a - 2b

meet at exactly one point, namely (-2,9)

Let's generate a few and plot. We'll do a vertical and horizontal an a couple of others.

a=-2, b=0, (b - 9)x - (a+2)y = -9a - 2b

-9x = 18

x = -2

a=0, b=9, (b - 9)x - (a+2)y = -9a - 2b

-2y = -18

y = 9

a=1, b=1, (b - 9)x - (a+2)y = -9a - 2b

-8x - 3y = -11

a=1, b=3, (b - 9)x - (a+2)y = -9a - 2b

-6x - 3y = -15

2x + y = 5

plot y=-7x+5, x = -2, y = 9, -8x - 3y = -11, 2x - y = 5

The equation y=-7x-5 and another equation have a solution of (-2,9). what is the second equation?

Answer from: Quest

D) the x-intercept represents adam's commission pay when he had zero total sales

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i think the answer is fried chicken ; >

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