Calculate the Slope of the Line Formed by Points (0,0) and (5,-2): An Analytical Approach

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

A negative slope means the line decreases as you move from left to right. Since point B(5,-2) is to the right and below point A(0,0), the line falls downward, giving us $ -\frac{2}{5} $.

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

No! You can choose either point as your first point. Just make sure you use the same order for both x and y coordinates. The slope will be the same either way.

Q: What does the fraction -2/5 actually mean?

The slope $ -\frac{2}{5} $ means for every 5 units right, the line goes 2 units down. The negative sign shows the downward direction.

Q: What if one of the points is on the origin like (0,0)?

Having a point at the origin makes calculations easier! When one coordinate is 0, you have fewer terms to subtract. Just follow the same slope formula as usual.

Slope Calculation with Coordinate Points

A straight line is drawn between the y axis and the straight line $y=-2$ to create a triangle.

The line passes through the points $B(5,-2),A\lparen0,0)$ .

Calculate the slope of the line.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

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

00:08 We will substitute the points according to the given data and solve to find the slope

00:27 And this is the solution to the question

Step-by-step written solution

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Understand the problem

A straight line is drawn between the y axis and the straight line $y=-2$ to create a triangle.

The line passes through the points $B(5,-2),A\lparen0,0)$ .

Calculate the slope of the line.

Step-by-step solution

To solve this problem, we'll calculate the slope using the slope formula:

Step 1: Identify the coordinates of the points. We have point $A(0, 0)$ and point $B(5, -2)$ .
Step 2: Apply the slope formula $m = \frac{y_2 - y_1}{x_2 - x_1}$ .
Step 3: Substitute the coordinates: $(x_1, y_1) = (0, 0)$ and $(x_2, y_2) = (5, -2)$ .

Now, let's work through each step:

The slope formula is:
$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-2 - 0}{5 - 0}$ .

This simplifies to:
$m = \frac{-2}{5}$ .

Therefore, the solution to the problem is $m = -\frac{2}{5}$ .

The correct answer choice is $-\frac{2}{5}$ .

Final Answer

$-\frac{2}{5}$

Key Points to Remember

Essential concepts to master this topic

Formula: Use m = (y₂ - y₁)/(x₂ - x₁) for any two points
Technique: Substitute A(0,0) and B(5,-2): m = (-2-0)/(5-0) = -2/5
Check: Negative slope means line falls from left to right ✓

Common Mistakes

Avoid these frequent errors

Mixing up the order of coordinates in the slope formula
Don't use (x₁ - x₂)/(y₁ - y₂) or switch point coordinates = wrong sign or value! This changes both the numerator and denominator incorrectly. Always keep the same point order: (y₂ - y₁)/(x₂ - x₁) consistently.

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 when the line goes down?

A negative slope means the line decreases as you move from left to right. Since point B(5,-2) is to the right and below point A(0,0), the line falls downward, giving us $-\frac{2}{5}$ .

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

No! You can choose either point as your first point. Just make sure you use the same order for both x and y coordinates. The slope will be the same either way.

What does the fraction -2/5 actually mean?

The slope $-\frac{2}{5}$ means for every 5 units right, the line goes 2 units down. The negative sign shows the downward direction.

How can I check if my slope calculation is correct?

Look at your points on a graph! From A(0,0) to B(5,-2), you move 5 right and 2 down. This gives $\frac{\text{rise}}{\text{run}} = \frac{-2}{5}$ ✓

What if one of the points is on the origin like (0,0)?

Having a point at the origin makes calculations easier! When one coordinate is 0, you have fewer terms to subtract. Just follow the same slope formula as usual.

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