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 $(-2,-4),(2,4)$

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Step-by-step video solution

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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

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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

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For the function in front of you, the slope is?

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!

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