Find the Line Passing Through (0,0) and (5,-5): Coordinate Geometry

Q: Why is the slope negative when the line goes down?

A negative slope means the line falls from left to right! As x increases from 0 to 5, y decreases from 0 to -5, so the line goes downward.

Q: What if one of the points is the origin?

Having a point at (0,0) actually makes the calculation easier! One of your subtractions will be minus zero, which doesn't change the value.

Slope Calculation with Origin Points

The line passes through the points $(0,0),(5,-5)$

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Step-by-step video solution

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00:00 Find the slope of the graph

00:03 For each point, we'll mark X and Y

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

00:24 We'll substitute appropriate values according to the given data, and solve to find the slope

00:43 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 $(0,0),(5,-5)$

Step-by-step solution

To find the slope of the line passing through the points $(0, 0)$ and $(5, -5)$ , we will use the slope formula. Let's follow these steps:

Step 1: Identify the points as $(x_1, y_1) = (0, 0)$ and $(x_2, y_2) = (5, -5)$ .
Step 2: Substitute these values into the slope formula $m = \frac{y_2 - y_1}{x_2 - x_1}$ .
Step 3: Perform the calculation:
$m = \frac{-5 - 0}{5 - 0} = \frac{-5}{5} = -1$

The calculation shows that the slope $m$ is $-1$ .

Therefore, the solution to the problem is $m = -1$ .

Final Answer

$m=-1$

Key Points to Remember

Essential concepts to master this topic

Formula: Use $m = \frac{y_2 - y_1}{x_2 - x_1}$ for any two points
Technique: $m = \frac{-5 - 0}{5 - 0} = \frac{-5}{5} = -1$
Check: Point (5,-5) should satisfy y = -1x: -5 = -1(5) ✓

Common Mistakes

Avoid these frequent errors

Subtracting coordinates in wrong order
Don't calculate $\frac{y_1 - y_2}{x_1 - x_2}$ = $\frac{0 - (-5)}{0 - 5} = \frac{5}{-5} = -1$ ! While this gives the same answer here, it creates confusion and wrong signs in other problems. Always use consistent order: $\frac{y_2 - y_1}{x_2 - x_1}$ .

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 is the slope negative when the line goes down?

A negative slope means the line falls from left to right! As x increases from 0 to 5, y decreases from 0 to -5, so the line goes downward.

Does it matter which point I call (x₁, y₁)?

No! You can choose either point as your starting point. Just make sure you're consistent - if (0,0) is (x₁, y₁), then (5,-5) must be (x₂, y₂).

What if one of the points is the origin?

Having a point at (0,0) actually makes the calculation easier! One of your subtractions will be minus zero, which doesn't change the value.

How can I visualize this slope of -1?

A slope of -1 means for every 1 unit you move right, you move 1 unit down. It's a 45-degree angle going downward from left to right.

Can I check my slope without graphing?

Yes! Pick any point on your line and use the slope to find another point. From (0,0), move right 1 and down 1 to get (1,-1). This should be on the same line as (5,-5).

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