Math  /  Geometry

QuestionFind the slope of the line passing through the points (5,2)(-5,-2) and (3,9)(3,-9). 78-\frac{7}{8}

Studdy Solution

STEP 1

What is this asking? We need to find how steep a line is that goes through two specific points. Watch out! Don't mix up the xx and yy coordinates!
Also, remember that subtracting a negative number is the same as adding a positive number.

STEP 2

1. Find the change in yy.
2. Find the change in xx.
3. Calculate the slope.

STEP 3

The change in yy is the difference between the yy-coordinates.
We can think of this as how much the line goes *up or down* as we move from left to right.
We'll call the change in yy "delta yy" or Δy\Delta y.

STEP 4

Let's **subtract** the yy-coordinate of the **first point** from the yy-coordinate of the **second point**: Δy=9(2) \Delta y = -9 - (-2)

STEP 5

Remember, subtracting a negative is the same as adding a positive! Δy=9+2=7 \Delta y = -9 + 2 = \mathbf{-7} So our **change in** yy is 7\mathbf{-7}.

STEP 6

The change in xx is the difference between the xx-coordinates.
We can think of this as how much the line goes *left or right* as we move from left to right.
We'll call the change in xx "delta xx" or Δx\Delta x.

STEP 7

Let's **subtract** the xx-coordinate of the **first point** from the xx-coordinate of the **second point**: Δx=3(5) \Delta x = 3 - (-5)

STEP 8

Again, subtracting a negative is the same as adding a positive! Δx=3+5=8 \Delta x = 3 + 5 = \mathbf{8} So our **change in** xx is 8\mathbf{8}.

STEP 9

The slope of a line is simply the **change in** yy *divided by* the **change in** xx.
It's often represented by the letter mm.
It's like figuring out how much the line goes up or down *for every one unit* it goes to the right.

STEP 10

We've already found Δy=7\Delta y = \mathbf{-7} and Δx=8\Delta x = \mathbf{8}, so now we just divide: m=ΔyΔx=78=78 m = \frac{\Delta y}{\Delta x} = \frac{-7}{8} = -\frac{7}{8}

STEP 11

The slope of the line passing through the points (5,2)(-5, -2) and (3,9)(3, -9) is 78-\frac{7}{8}.

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