Calculate the Slope: Analyzing a Linear Function in the Coordinate Plane

Linear Functions with Visual Slope Identification

For the function in front of you, the slope is?

XY

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Choose whether the slope is negative or positive
00:07 The function is decreasing, therefore the slope is negative
00:17 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

For the function in front of you, the slope is?

XY

2

Step-by-step solution

To solve this problem, we need to determine the slope of the line depicted on the graph.

First, understand that the slope of a line on a coordinate plane indicates how steep the line is and the direction it is heading. Specifically:

  • A positive slope means the line rises as it goes from left to right.
  • A negative slope means the line falls as it goes from left to right.

Let's examine the graph given:

  • We see that the line starts at a higher point on the left and descends to a lower point on the right side.
  • As we move from the left side of the graph towards the right, the line goes downwards.

This downward trajectory clearly indicates a negative slope because the line is declining as we move horizontally left to right.

Therefore, the slope of this function is Negative.

The correct answer is, therefore, Negative slope.

3

Final Answer

Negative slope

Key Points to Remember

Essential concepts to master this topic
  • Rule: Positive slopes rise left to right, negative slopes fall
  • Technique: Trace the line direction: down from left to right = negative
  • Check: Pick two points and calculate: falling y-values confirm negative slope ✓

Common Mistakes

Avoid these frequent errors
  • Confusing the direction when reading the graph
    Don't read the line from right to left or focus on steepness alone = wrong slope sign! This leads to calling downward lines positive. Always trace from left to right and focus on whether the line rises or falls.

Practice Quiz

Test your knowledge with interactive questions

For the function in front of you, the slope is?

XY

FAQ

Everything you need to know about this question

How do I remember which direction to read the graph?

+

Always read from left to right, just like reading text! Start at the left side of the line and follow it to the right. If it goes up, it's positive. If it goes down, it's negative.

What if the line looks really steep - does that affect the sign?

+

The steepness doesn't change the sign of the slope! A very steep line going down is still negative, and a gentle line going up is still positive. Focus on direction, not steepness.

Can I use specific points to double-check my answer?

+

Absolutely! Pick any two points on the line and use the slope formula: y2y1x2x1 \frac{y_2 - y_1}{x_2 - x_1} . If you get a negative number, the slope is negative.

What does negative slope mean in real life?

+

Negative slope shows a decreasing relationship! For example, as time increases, the temperature decreases, or as you spend more money, your savings decrease.

Is there a difference between 'negative slope' and 'downward slope'?

+

No difference at all! Both terms mean the same thing - the line falls as you move from left to right. Negative slope is the mathematical term, while downward slope describes what you see visually.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Linear Functions questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime

More Questions

Click on any question to see the complete solution with step-by-step explanations