Determine the Slope from a Linear Graph: Visual Mathematics Practice

Slope Direction with Visual Graph 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
00:04 Let's select 2 points on the graph
00:08 Let's pay attention to the direction of progression, to know what comes before what
00:13 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

For this problem, we need to determine the nature of the slope for a given straight line on a graph.

Based on the graph provided, the red line starts at a higher point on the left (Y-axis) and moves downward toward a lower point on the right (X-axis). This indicates that as one moves from left to right across the graph, the function decreases in value. Consequently, this is typical of a line that has a negative slope.

The slope of a line is typically defined as the "rise over the run," or the ratio of the change in the vertical direction to the change in the horizontal direction. Here, as we proceed from left to right, the line goes "downwards" (negative rise), establishing a negative slope.

Thus, we can conclude that the slope of the line is negative.

Therefore, the solution to the problem is Negative slope.

3

Final Answer

Negative slope

Key Points to Remember

Essential concepts to master this topic
  • Visual Rule: Rising left-to-right means positive, falling means negative slope
  • Technique: Track line direction: this line falls downward as x increases
  • Check: Left point higher than right point confirms negative slope ✓

Common Mistakes

Avoid these frequent errors
  • Confusing slope direction with line position
    Don't focus on where the line is located on the graph = wrong slope determination! Position doesn't matter - only the direction matters. Always follow the line from left to right to see if it rises or falls.

Practice Quiz

Test your knowledge with interactive questions

What is the solution to the following inequality?

\( 10x-4≤-3x-8 \)

FAQ

Everything you need to know about this question

How do I tell if a line has positive or negative slope just by looking?

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Follow the line from left to right like reading a book. If it goes upward, the slope is positive. If it goes downward, the slope is negative. This line clearly goes down from left to right!

What if the line is steep? Does that change if it's positive or negative?

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Steepness doesn't change the sign! A steep upward line is still positive, and a steep downward line is still negative. The angle only affects how large the slope value is, not whether it's positive or negative.

Can I use any two points on the line to check my answer?

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Yes! Pick any two points 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. If positive, the slope is positive.

What does it mean when a line has negative slope in real life?

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Negative slope means as one thing increases, the other decreases. For example: as time increases, the temperature might decrease, or as you spend more money, your savings account balance goes down.

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

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No difference at all! Negative slope and downward sloping mean exactly the same thing. Both describe a line that falls as you move from left to right across the graph.

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