Find the Line Through Points (-2,-4) and (2,4): Coordinate Geometry

Q: What does a slope of 2 actually mean?

A slope of 2 means the line rises 2 units up for every 1 unit right. It's a fairly steep upward slope. You can see this with our points: from (-2,-4) to (2,4), we go 4 units right and 8 units up, giving us $\frac{8}{4} = 2$.

Q: How do I handle the double negative in the calculation?

When you see $4 - (-4)$, remember that subtracting a negative is adding. So $4 - (-4) = 4 + 4 = 8$. Same with the denominator: $2 - (-2) = 2 + 2 = 4$.

Q: Can I use a different formula to find the slope?

The slope formula $m = \frac{y_2 - y_1}{x_2 - x_1}$ is the standard method for two points. While you could think about it as "rise over run" by counting on a graph, the formula is more accurate and works for any two points.

Slope Calculation with Integer Coordinates

The line passes through the points $(-2,-4),(2,4)$

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the slope of the graph

00:04 We'll use the formula to find the slope using 2 points on the graph

00:11 For each point we'll mark X and Y

00:27 We'll substitute appropriate values according to the given data, and solve to find the slope

00:48 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

The line passes through the points $(-2,-4),(2,4)$

Step-by-step solution

To find the slope of the line that passes through the points $(-2, -4)$ and $(2, 4)$ , we use the slope formula:

The slope $m$ is calculated using $m = \frac{y_2 - y_1}{x_2 - x_1}$ .
Plugging in the given points, $(x_1, y_1) = (-2, -4)$ and $(x_2, y_2) = (2, 4)$ , we have:

$m = \frac{4 - (-4)}{2 - (-2)}$

$m = \frac{4 + 4}{2 + 2}$

$m = \frac{8}{4}$

After simplifying, we find:

$m = 2$

Therefore, the slope of the line is $m = 2$ , corresponding to choice 3.

Final Answer

$m=2$

Key Points to Remember

Essential concepts to master this topic

Formula: Use slope formula $m = \frac{y_2 - y_1}{x_2 - x_1}$
Technique: For points (-2,-4) and (2,4): $m = \frac{4-(-4)}{2-(-2)} = \frac{8}{4} = 2$
Check: Rise over run: up 8 units, right 4 units gives slope 2 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to handle negative signs correctly
Don't calculate 4 - (-4) as 4 - 4 = 0! This ignores the negative sign and gives slope 0 instead of 2. Always remember that subtracting a negative is the same as adding: 4 - (-4) = 4 + 4 = 8.

Practice Quiz

Test your knowledge with interactive questions

Look at the linear function represented in the diagram.

When is the function positive?

FAQ

Everything you need to know about this question

Why do I get different answers when I switch the points?

You shouldn't! The slope is the same regardless of which point you call $(x_1, y_1)$ . Just make sure you're consistent - if you start with (-2,-4) as point 1, use (2,4) as point 2 throughout the calculation.

What does a slope of 2 actually mean?

A slope of 2 means the line rises 2 units up for every 1 unit right. It's a fairly steep upward slope. You can see this with our points: from (-2,-4) to (2,4), we go 4 units right and 8 units up, giving us $\frac{8}{4} = 2$ .

How do I handle the double negative in the calculation?

When you see $4 - (-4)$ , remember that subtracting a negative is adding. So $4 - (-4) = 4 + 4 = 8$ . Same with the denominator: $2 - (-2) = 2 + 2 = 4$ .

Can I use a different formula to find the slope?

The slope formula $m = \frac{y_2 - y_1}{x_2 - x_1}$ is the standard method for two points. While you could think about it as "rise over run" by counting on a graph, the formula is more accurate and works for any two points.

What if my points were in a different order?

The slope will be the same! Try it: using (2,4) as point 1 and (-2,-4) as point 2 gives $m = \frac{-4-4}{-2-2} = \frac{-8}{-4} = 2$ . Same answer!

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Linear Functions questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime