Calculate the Slope: Analyzing a Linear Function from its Graph

Slope Direction with Visual Analysis

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

XY

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Choose whether the slope is negative or positive
00:05 Let's select 2 points on the graph
00:12 Let's pay attention to the direction of progression, to know what comes before what
00:15 The function is increasing, therefore the slope is positive
00:19 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 determine the slope of the line segment shown in the graph, follow these steps:

  • Identify the line segment on the graph; it's shown as a red line from one point to another.
  • Examine the direction the line segment travels from the leftmost point to the rightmost point.
  • Visually analyze whether the line segment is rising or falling as it moves from left to right.

Here is the detailed analysis:
- The red line segment starts lower on the left side and ends higher on the right side.
- This suggests that as we move from left to right, the line is rising.
- In terms of slope, a line that rises as it moves from left to right has a positive slope.

Therefore, the slope of the line segment is positive.

Thus, the correct answer is 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 Technique: Follow the red line from left point to right point
  • Check: Higher endpoint on right confirms positive slope ✓

Common Mistakes

Avoid these frequent errors
  • Confusing rise direction with slope sign
    Don't think a line going down from left to right has positive slope = backwards reasoning! This leads to choosing negative when the answer is positive. Always remember: rising left-to-right means positive slope, falling left-to-right means negative slope.

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 quickly tell if a slope is positive or negative?

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Use the "left-to-right rule"! Start at the leftmost point and trace to the rightmost point. If you go upward, the slope is positive. If you go downward, the slope is negative.

What if the line looks steep? Does that change the slope sign?

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Steepness affects the magnitude (size) of the slope, but not the sign! A steep upward line still has positive slope, just a larger positive number like +5 instead of +0.5.

Can I use the slope formula instead of visual analysis?

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Yes! If you have coordinates, use m=y2y1x2x1 m = \frac{y_2 - y_1}{x_2 - x_1} . But for quick identification, visual analysis is faster and just as reliable.

What does it mean if a line is horizontal?

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A horizontal line has zero slope because it doesn't rise or fall. A vertical line has undefined slope because you can't divide by zero in the slope formula.

How is this different from finding the actual slope value?

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This question asks for slope direction (positive or negative), not the exact number. To find the actual slope value, you'd need specific coordinates and the slope formula.

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