Line Through Points (-5,10) and (0,0): Coordinate Geometry Analysis

Q: Why is the slope negative when the line goes up from left to right?

The line actually goes down from left to right! Starting at (-5, 10) and moving to (0, 0), you move right 5 units but down 10 units, giving a negative slope.

Q: Can I use either point as (x₁, y₁)?

Yes! The slope formula works with either point as the first point. Just make sure to keep the same order for both x and y coordinates: $ \frac{y_2 - y_1}{x_2 - x_1} $

Q: What does a slope of -2 actually mean?

A slope of -2 means for every 1 unit right, the line goes 2 units down. It's twice as steep as a slope of -1 and goes in the downward direction.

Q: What if I get a fraction that doesn't simplify?

That's normal! In this problem $ \frac{-10}{5} $ simplifies to -2, but many slope problems give fractions like $ \frac{3}{7} $ that don't reduce further.

Slope Calculation with Coordinate Points

The line passes through the points $(-5,10),(0,0)$

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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

00:10 For each point we'll mark X and Y

00:20 We'll substitute appropriate values according to the given data, and solve to find the slope

00:34 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 $(-5,10),(0,0)$

Step-by-step solution

The problem asks us to find the slope of the line passing through the points $(-5, 10)$ and $(0, 0)$ . To solve this, we'll follow these steps:

Step 1: Note the coordinates of the two points. Let $(x_1, y_1) = (-5, 10)$ and $(x_2, y_2) = (0, 0)$ .
Step 2: Apply the slope formula $m = \frac{y_2 - y_1}{x_2 - x_1}$ .
Step 3: Substitute the values from the points into the formula and simplify.

Now, let's substitute and compute the slope:

$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - 10}{0 - (-5)} = \frac{-10}{5}$ .

Simplifying, we get $m = -2$ .

Therefore, the slope of the line is $m = -2$ .

Final Answer

$m=-2$

Key Points to Remember

Essential concepts to master this topic

Formula: Use m = (y₂ - y₁)/(x₂ - x₁) for slope between points
Technique: Substitute (-5,10) and (0,0): m = (0-10)/(0-(-5)) = -10/5
Check: Rise of -10 over run of 5 gives slope -2 ✓

Common Mistakes

Avoid these frequent errors

Subtracting coordinates in wrong order
Don't calculate (x₁ - x₂)/(y₁ - y₂) or mix up the order = wrong slope sign! This reverses the fraction and gives incorrect positive/negative values. Always use consistent order: (y₂ - y₁)/(x₂ - x₁).

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 is the slope negative when the line goes up from left to right?

The line actually goes down from left to right! Starting at (-5, 10) and moving to (0, 0), you move right 5 units but down 10 units, giving a negative slope.

Can I use either point as (x₁, y₁)?

Yes! The slope formula works with either point as the first point. Just make sure to keep the same order for both x and y coordinates: $\frac{y_2 - y_1}{x_2 - x_1}$

What does a slope of -2 actually mean?

A slope of -2 means for every 1 unit right, the line goes 2 units down. It's twice as steep as a slope of -1 and goes in the downward direction.

How can I visualize this on a graph?

Plot both points: (-5, 10) is in the upper left, (0, 0) is at the origin. Draw a line connecting them - it clearly slopes downward from left to right!

What if I get a fraction that doesn't simplify?

That's normal! In this problem $\frac{-10}{5}$ simplifies to -2, but many slope problems give fractions like $\frac{3}{7}$ that don't reduce further.

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