Calculate Slope Between Points (-6,1) and (2,4): Step-by-Step Solution

Q: Why do I subtract the coordinates in a specific order?

The slope formula requires consistent ordering: if you use $ (x_1, y_1) $ and $ (x_2, y_2) $, then calculate $ \frac{y_2 - y_1}{x_2 - x_1} $. Mixing up the order gives you the negative of the correct slope!

Q: What does it mean when I subtract a negative number?

Subtracting a negative is the same as adding the positive! So $ 2-(-6) = 2+6 = 8 $. Think of it as: "take away negative 6" means "add positive 6."

Q: How do I know if my slope is positive or negative?

Look at the line's direction: if it goes up from left to right, the slope is positive. If it goes down from left to right, the slope is negative. Here, going from (-6,1) to (2,4) goes up, so slope is positive.

Q: Can I switch which point is (x₁,y₁) and which is (x₂,y₂)?

Yes! You'll get the same answer either way. Try it: $ \frac{1-4}{-6-2} = \frac{-3}{-8} = \frac{3}{8} $. Just be consistent with your choice throughout the calculation.

Q: Why is my answer a fraction instead of a decimal?

Fractions are the exact answer! $ \frac{3}{8} = 0.375 $, but keeping it as a fraction shows the precise relationship. Most math problems prefer fractional answers when possible.

Slope Formula with Negative Coordinates

Calculate the slope of a straight line that passes through the points $(-6,1),(2,4)$ .

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the slope of the graph

00:05 We'll find the slope using 2 points

00:15 We'll use the formula to find the slope using 2 points

00:25 We'll substitute appropriate values according to the given data and solve for the slope

00:47 This is the slope of the graph

00:50 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Calculate the slope of a straight line that passes through the points $(-6,1),(2,4)$ .

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Identify the coordinates of the given points.
Step 2: Substitute these values into the slope formula.
Step 3: Simplify to find the slope.

Now, let's work through each step:
Step 1: Given points are $(-6, 1)$ and $(2, 4)$ . Thus, we have:
$x_1 = -6, y_1 = 1$ , $x_2 = 2, y_2 = 4$ .
Step 2: Apply the slope formula:
$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{4 - 1}{2 - (-6)}$
Step 3: Simplify:
Calculate the numerator: $4 - 1 = 3$ .
Calculate the denominator: $2 - (-6) = 2 + 6 = 8$ .
Thus, the slope $m$ is:
$m = \frac{3}{8}$

Therefore, the solution to the problem is $\frac{3}{8}$ .

Final Answer

$\frac{3}{8}$

Key Points to Remember

Essential concepts to master this topic

Formula: Slope equals rise over run: $m = \frac{y_2 - y_1}{x_2 - x_1}$
Technique: Subtract coordinates carefully: $\frac{4-1}{2-(-6)} = \frac{3}{8}$
Check: Verify denominator calculation: $2-(-6) = 2+6 = 8$ ✓

Common Mistakes

Avoid these frequent errors

Incorrect handling of negative coordinates in subtraction
Don't calculate $2-(-6)$ as $2-6 = -4$ = wrong slope of $-\frac{3}{4}$ ! Subtracting a negative means adding the positive. Always remember: $2-(-6) = 2+6 = 8$ .

Practice Quiz

Test your knowledge with interactive questions

What is the solution to the following inequality?

$$ 10x-4\leq-3x-8 $$

FAQ

Everything you need to know about this question

Why do I subtract the coordinates in a specific order?

The slope formula requires consistent ordering: if you use $(x_1, y_1)$ and $(x_2, y_2)$ , then calculate $\frac{y_2 - y_1}{x_2 - x_1}$ . Mixing up the order gives you the negative of the correct slope!

What does it mean when I subtract a negative number?

Subtracting a negative is the same as adding the positive! So $2-(-6) = 2+6 = 8$ . Think of it as: "take away negative 6" means "add positive 6."

How do I know if my slope is positive or negative?

Look at the line's direction: if it goes up from left to right, the slope is positive. If it goes down from left to right, the slope is negative. Here, going from (-6,1) to (2,4) goes up, so slope is positive.

Can I switch which point is (x₁,y₁) and which is (x₂,y₂)?

Yes! You'll get the same answer either way. Try it: $\frac{1-4}{-6-2} = \frac{-3}{-8} = \frac{3}{8}$ . Just be consistent with your choice throughout the calculation.

Why is my answer a fraction instead of a decimal?

Fractions are the exact answer! $\frac{3}{8} = 0.375$ , but keeping it as a fraction shows the precise relationship. Most math problems prefer fractional answers when possible.

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