Finding the Slope of a Linear Function from Its Graph

Slope Determination with Visual Graph Analysis

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
00:03 Let's choose 2 points on the graph
00:08 Let's pay attention to the direction of progression, to know what comes before what
00:14 The function is increasing, therefore the slope is positive
00:18 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, let's analyze the given graph of the function to determine the slope's sign.

The slope of a line on a graph indicates the line's direction. A line with a positive slope rises as it moves from left to right, indicating that for every step taken to the right (along the x-axis), we move upward. Conversely, a line with a negative slope falls as it moves from left to right, meaning each step to the right results in moving downward.

Examining the graph provided, the red line starts higher on the left and goes downward towards the right visually. This indicates that the line is rising as it goes from left to right, which confirms it has a positive slope.

Therefore, the solution to the problem, regarding the slope of the line, is that it is a Positive slope.

3

Final Answer

Positive slope

Key Points to Remember

Essential concepts to master this topic
  • Direction Rule: Rising left to right means positive slope
  • Visual Method: Follow the line: goes up as x increases
  • Check: Pick two points and verify rise over run ✓

Common Mistakes

Avoid these frequent errors
  • Confusing visual direction with slope sign
    Don't assume a line going down on the screen means negative slope = wrong interpretation! The line appears to go down visually but actually rises from left to right. Always trace the line's direction as x increases from left to right.

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 can I tell if a slope is positive or negative just by looking?

+

Look at the line's direction as you move from left to right along the x-axis. If the line goes up, it's positive. If it goes down, it's negative.

The line looks like it's going downward - why is this positive?

+

The key is following the line from left to right! Even though it visually appears to go down on your screen, mathematically it's rising as x increases, making it a positive slope.

Can I calculate the exact slope value from this graph?

+

Yes! Pick any two clear points on the line, then use the formula: slope=riserun=y2y1x2x1 \text{slope} = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}

What if the line looks steep - does that affect whether it's positive or negative?

+

Steepness only affects the magnitude of the slope, not its sign! A steep line can be positive or negative - it's all about the direction from left to right.

How do I avoid getting confused by the visual appearance?

+

Always use the left-to-right rule: trace your finger along the line from left to right. If your finger moves up, it's positive. If it moves down, it's negative.

🌟 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