Calculate the Slope: Linear Function through Points (0,7) and (-4,-9)

Q: Does it matter which point I call (x₁, y₁) and which I call (x₂, y₂)?

No, it doesn't matter! You can assign either point as $ (x_1, y_1) $. Just be consistent - use the same point's coordinates first in both numerator and denominator.

Q: Why did the negative signs cancel out in this problem?

When you divide negative by negative, you get positive! $ \frac{-16}{-4} = +4 $ because the signs are the same in numerator and denominator.

Q: What does a slope of 4 actually mean?

A slope of 4 means the line goes up 4 units for every 1 unit it moves right. It's a steep upward line since the slope is greater than 1.

Q: What if I get a fraction as my slope?

Fractional slopes are completely normal! For example, $ \frac{3}{2} $ means up 3, right 2. Just make sure to simplify the fraction to lowest terms.

Slope Calculation with Given Coordinate Points

In the drawing of the graph of the linear function passing through the points $A(0,7)$ y $B(-4,-9)$

Find the slope of the graph.

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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 graph

00:03 We will find the slope using 2 points

00:17 We will use the formula to find the slope using 2 points

00:25 We will substitute appropriate values according to the given data and solve to find the slope

00:42 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

In the drawing of the graph of the linear function passing through the points $A(0,7)$ y $B(-4,-9)$

Find the slope of the graph.

Step-by-step solution

To find the slope ( $m$ ) of the line passing through the points $A(0,7)$ and $B(-4,-9)$ , we apply the slope formula:

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

First, assign the coordinates to the two points:

$(x_1, y_1) = (0, 7)$
$(x_2, y_2) = (-4, -9)$

Next, substitute these into the slope formula:

m = \frac{-9 - 7}{-4 - 0}

Simplify the expression:

m = \frac{-16}{-4}

The negative signs in the numerator and denominator cancel out:

m = \frac{16}{4}

Finally, divide to find the slope:

m = 4

Therefore, the slope of the line passing through points $A(0,7)$ and $B(-4,-9)$ is $4$ .

Final Answer

$4$

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: Substitute coordinates: $\frac{-9 - 7}{-4 - 0} = \frac{-16}{-4} = 4$
Check: Negative divided by negative equals positive: $\frac{-16}{-4} = 4$ ✓

Common Mistakes

Avoid these frequent errors

Mixing up coordinate order in subtraction
Don't randomly subtract coordinates like $\frac{7 - (-9)}{0 - (-4)}$ = 4! This accidentally gives the right answer but uses wrong method. Always consistently use $(x_1, y_1)$ and $(x_2, y_2)$ in the same order for both numerator and denominator.

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

Does it matter which point I call (x₁, y₁) and which I call (x₂, y₂)?

No, it doesn't matter! You can assign either point as $(x_1, y_1)$ . Just be consistent - use the same point's coordinates first in both numerator and denominator.

Why did the negative signs cancel out in this problem?

When you divide negative by negative, you get positive! $\frac{-16}{-4} = +4$ because the signs are the same in numerator and denominator.

What does a slope of 4 actually mean?

A slope of 4 means the line goes up 4 units for every 1 unit it moves right. It's a steep upward line since the slope is greater than 1.

How can I check if my slope calculation is correct?

Use the slope to verify: starting from point A(0,7), move right 1 unit and up 4 units. You should get closer to point B. Or substitute both points into $y = mx + b$ and see if they work!

What if I get a fraction as my slope?

Fractional slopes are completely normal! For example, $\frac{3}{2}$ means up 3, right 2. Just make sure to simplify the fraction to lowest terms.

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Calculate the Slope: Linear Function through Points (0,7) and (-4,-9)

Slope Calculation with Given Coordinate 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

Does it matter which point I call (x₁, y₁) and which I call (x₂, y₂)?

Why did the negative signs cancel out in this problem?

What does a slope of 4 actually mean?

How can I check if my slope calculation is correct?

What if I get a fraction as my slope?

🌟 Unlock Your Math Potential

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