Math  /  Algebra

QuestionFind the slope of the line that passes through (7,6)(7,6) and (5,3)(5,3). Simplify your answer and write it as a proper fraction, improper fraction, or intes \square In Submit

Studdy Solution

STEP 1

What is this asking? We need to find how steep a line is that goes through two given points. Watch out! Don't mix up the xx and yy coordinates when calculating the slope!

STEP 2

1. Label the points
2. Slope formula
3. Calculate the slope

STEP 3

Let's **label** our two points to keep things organized.
We'll call (7,6)(7,6) point 1, so x1=7x_1 = 7 and y1=6y_1 = 6.
And we'll call (5,3)(5,3) point 2, so x2=5x_2 = 5 and y2=3y_2 = 3.
This helps us plug the right numbers into the right spots in the formula!

STEP 4

Remember, the **slope**, often represented by mm, is the "rise over run," or how much the line goes up or down divided by how much it goes across.
The **formula** is: m=y2y1x2x1 m = \frac{y_2 - y_1}{x_2 - x_1} This tells us how much the yy-value changes compared to how much the xx-value changes.

STEP 5

Now, let's **plug in** our values.
We have x1=7x_1 = 7, y1=6y_1 = 6, x2=5x_2 = 5, and y2=3y_2 = 3.
Substituting these into the slope formula, we get: m=3657 m = \frac{3 - 6}{5 - 7}

STEP 6

**Subtract** the numbers in the numerator and the denominator: m=32 m = \frac{-3}{-2}

STEP 7

A negative divided by a negative is a positive!
So, we **simplify** to: m=32 m = \frac{3}{2}

STEP 8

The slope of the line passing through (7,6)(7,6) and (5,3)(5,3) is 32\frac{3}{2}.

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