Calculate the Slope of the Line Passing through B(5,0) and A(0,10)

Q: Why is the slope negative in this problem?

The slope is negative because the line goes downward from left to right. Point A(0,10) is higher than point B(5,0), so as x increases, y decreases!

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

No! You can choose either point as (x₁,y₁), just be consistent. Whether you use A first or B first, you'll get the same slope of $ -2 $.

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

A slope of $ -2 $ means for every 1 unit you move right, the line drops down 2 units. It's a fairly steep downward line!

Q: What if I get a fraction for the slope?

That's completely normal! Many lines have fractional slopes like $ \frac{2}{3} $ or $ -\frac{1}{4} $. Just make sure to simplify the fraction if possible.

Slope Calculation with Coordinate Points

Calculate the slope of the line that creates a right triangle with the x and y axes and passes through the points $B(5,0),A\lparen0,10)$ .

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Step-by-step video solution

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00:00 Find the slope of the line

00:03 We will use the formula to find the slope of a line using 2 points

00:11 We will substitute the points according to the given data and solve to find the slope

00:29 And this is the solution to the question

Step-by-step written solution

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Understand the problem

Calculate the slope of the line that creates a right triangle with the x and y axes and passes through the points $B(5,0),A\lparen0,10)$ .

Step-by-step solution

To solve this problem, we'll determine the slope of the line that passes through the points $A(0, 10)$ and $B(5, 0)$ . The slope of a line passing through two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by:

$m = \frac{y_2 - y_1}{x_2 - x_1}$ .

We identify the coordinates of our points:

$(x_1, y_1) = (5, 0)$
$(x_2, y_2) = (0, 10)$ .

Substitute these coordinates into the slope formula:

$m = \frac{10 - 0}{0 - 5}$ .

Simplifying the equation gives:

$m = \frac{10}{-5} = -2$ .

Thus, the slope of the line is $-2$ .

Therefore, the solution to the problem is $m = -2$ .

Final Answer

$-2$

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: Subtract coordinates: $\frac{10-0}{0-5} = \frac{10}{-5} = -2$
Check: Negative slope means line goes down from left to right ✓

Common Mistakes

Avoid these frequent errors

Subtracting coordinates in wrong order
Don't switch the order like $\frac{0-10}{5-0} = -2$ = wrong calculation! This mixes up which point is (x₁,y₁) and which is (x₂,y₂), giving incorrect signs or values. Always keep the same point order: if B(5,0) is first, use B's coordinates as (x₁,y₁) throughout.

Practice Quiz

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Look at the linear function represented in the diagram.

When is the function positive?

FAQ

Everything you need to know about this question

Why is the slope negative in this problem?

The slope is negative because the line goes downward from left to right. Point A(0,10) is higher than point B(5,0), so as x increases, y decreases!

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

No! You can choose either point as (x₁,y₁), just be consistent. Whether you use A first or B first, you'll get the same slope of $-2$ .

What does a slope of -2 actually mean?

A slope of $-2$ means for every 1 unit you move right, the line drops down 2 units. It's a fairly steep downward line!

How can I double-check my slope calculation?

Use the slope formula backwards: start at one point and move according to your slope. From B(5,0), move left 5 units and up 10 units. You should land exactly at A(0,10)!

What if I get a fraction for the slope?

That's completely normal! Many lines have fractional slopes like $\frac{2}{3}$ or $-\frac{1}{4}$ . Just make sure to simplify the fraction if possible.

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