Calculate Slope of Linear Function: Points A(0,-10) and B(4,1)

Q: Why do we subtract y-coordinates in the numerator and x-coordinates in the denominator?

The slope formula measures rise over run. The numerator (y₂ - y₁) gives you how much the line goes up or down, while the denominator (x₂ - x₁) tells you how far it moves left or right.

Q: What does it mean that the slope is positive?

A positive slope like $ 2\frac{3}{4} $ means the line goes upward from left to right. For every 4 units you move right, the line goes up 11 units!

Q: Can I use the points in reverse order?

Yes! You can use B as point 1 and A as point 2: $ \frac{-10-1}{0-4} = \frac{-11}{-4} = \frac{11}{4} $. Just be consistent with which point is first in both numerator and denominator.

Q: How do I convert the improper fraction to a mixed number?

Divide the numerator by the denominator: 11 ÷ 4 = 2 with remainder 3. So $ \frac{11}{4} = 2\frac{3}{4} $. The quotient becomes the whole number, remainder becomes the new numerator!

Q: What if one of my coordinates is zero?

Zero coordinates make the calculation easier! In this problem, A(0,-10) has x = 0, so the denominator becomes 4-0 = 4. Don't worry about zeros - just substitute them like any other number.

Slope Calculation with Two Given Points

In the drawing of the graph of the linear function passing through the points $A(0,-10)$ y $B(4,1)$

Find the slope of the graph.

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Step-by-step video solution

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00:00 Find the slope of the graph

00:05 We will find the slope using 2 points

00:20 We will use the formula to find the slope using 2 points

00:29 We will substitute appropriate values according to the given data and solve to find the slope

00:51 And this is the solution to the question

Step-by-step written solution

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Understand the problem

In the drawing of the graph of the linear function passing through the points $A(0,-10)$ y $B(4,1)$

Find the slope of the graph.

Step-by-step solution

To solve this problem, we need to calculate the slope of the line passing through the points $A(0, -10)$ and $B(4, 1)$ .

The formula for the slope $m$ of a line that passes through two points $(x_1, y_1)$ and $(x_2, y_2)$ is:

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

Given the points $A(0, -10)$ and $B(4, 1)$ , we identify:

$x_1 = 0, y_1 = -10$
$x_2 = 4, y_2 = 1$

Substituting these values into the slope formula, we have:

m = \frac{1 - (-10)}{4 - 0}

This simplifies to:

m = \frac{1 + 10}{4} = \frac{11}{4}

The fraction $\frac{11}{4}$ can be converted to a mixed number:

\frac{11}{4} = 2\frac{3}{4}

Therefore, the slope of the graph is $\bm{2\frac{3}{4}}$ .

Final Answer

$2\frac{3}{4}$

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,-10) and B(4,1) to get (1-(-10))/(4-0) = 11/4
Check: Convert 11/4 to mixed number: 11 ÷ 4 = 2 remainder 3, so 2¾ ✓

Common Mistakes

Avoid these frequent errors

Subtracting coordinates in wrong order
Don't calculate (y₁ - y₂)/(x₁ - x₂) = (-10-1)/(0-4) = -11/-4 = wrong sign! This reverses both numerator and denominator, giving the opposite slope direction. Always subtract consistently: second point minus first point in both numerator and denominator.

Practice Quiz

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What is the solution to the following inequality?

$$ 10x-4\leq-3x-8 $$

FAQ

Everything you need to know about this question

Why do we subtract y-coordinates in the numerator and x-coordinates in the denominator?

The slope formula measures rise over run. The numerator (y₂ - y₁) gives you how much the line goes up or down, while the denominator (x₂ - x₁) tells you how far it moves left or right.

What does it mean that the slope is positive?

A positive slope like $2\frac{3}{4}$ means the line goes upward from left to right. For every 4 units you move right, the line goes up 11 units!

Can I use the points in reverse order?

Yes! You can use B as point 1 and A as point 2: $\frac{-10-1}{0-4} = \frac{-11}{-4} = \frac{11}{4}$ . Just be consistent with which point is first in both numerator and denominator.

How do I convert the improper fraction to a mixed number?

Divide the numerator by the denominator: 11 ÷ 4 = 2 with remainder 3. So $\frac{11}{4} = 2\frac{3}{4}$ . The quotient becomes the whole number, remainder becomes the new numerator!

What if one of my coordinates is zero?

Zero coordinates make the calculation easier! In this problem, A(0,-10) has x = 0, so the denominator becomes 4-0 = 4. Don't worry about zeros - just substitute them like any other number.

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Calculate Slope of Linear Function: Points A(0,-10) and B(4,1)

Slope Calculation with Two Given Points

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why do we subtract y-coordinates in the numerator and x-coordinates in the denominator?

What does it mean that the slope is positive?

Can I use the points in reverse order?

How do I convert the improper fraction to a mixed number?

What if one of my coordinates is zero?

🌟 Unlock Your Math Potential

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