What is the intersection point of the lines y = 4p - 9537 and y=-p + 500?

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First off, let's understand what this whole intersection - point thing is all about. When we talk about two lines on a graph, the intersection point is where those two lines meet. Mathematically, at that specific point, the y - values of both lines are the same. So, since both equations are equal to y, we can set them equal to each other. That is, 4p - 9537 = -p + 500.

Now, we need to solve this equation for p. The goal is to get all the p terms on one side and the numbers on the other side. Let's add p to both sides of the equation. When we do that, we get 4p + p- 9537=-p + p+ 500. Simplifying this gives us 5p - 9537 = 500.

Next, we add 9537 to both sides of the equation. We have 5p-9537 + 9537 = 500+9537. This simplifies to 5p = 10037.

To find the value of p, we divide both sides of the equation by 5. So, p = 10037/5 = 2007.4.

Now that we've found the value of p, we can find the corresponding y - value. We can use either of the two original equations. Let's use the equation y=-p + 500. Substitute p = 2007.4 into this equation. We get y=-2007.4 + 500. So, y=-1507.4.

The intersection point of the two lines y = 4p - 9537 and y=-p + 500 is (p,y)=(2007.4, - 1507.4).

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References

• Standard Algebra Textbooks (covering linear equations and their solutions)