Finding the Slope: Linear Function from Coordinate Graph

Slope Determination 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
00:03 Let's select 2 points on the graph
00:10 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

To determine the slope of the line, we'll examine the direction of the line segment on the graph:

  • The line depicted moves from the top left, passing through a point with higher y y -coordinate values, to the bottom right, ending at a point with lower y y -coordinate values.
  • This movement indicates that as x x increases (the direction to the right along the x x -axis), the y y -coordinate decreases.
  • When the y y -value reduces as the x x -value grows, the slope m m is negative.

Since the line descends from left to right, the slope of the line is negative.

Therefore, the slope of the function is a negative slope.

3

Final Answer

Negative slope

Key Points to Remember

Essential concepts to master this topic
  • Direction Rule: Line going down left-to-right means negative slope
  • Technique: Check if y y decreases as x x increases across graph
  • Check: Trace line movement: higher left to lower right = negative ✓

Common Mistakes

Avoid these frequent errors
  • Confusing line direction with slope sign
    Don't think upward-slanting lines always mean positive slope = wrong interpretation! The direction depends on your viewing perspective. Always check if y y values decrease as x x values increase when moving left to right.

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 can I quickly tell if a slope is positive or negative?

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Use the "left-to-right rule": If the line goes up as you move from left to right, it's positive. If it goes down, it's negative. Think of it like climbing a hill (positive) or going downhill (negative)!

What if the line looks diagonal but I'm not sure which direction?

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Pick any two points on the line and compare their y y -coordinates. If the rightward point has a smaller y y -value, the slope is negative. If it has a larger y y -value, the slope is positive.

Does the steepness of the line matter for determining positive or negative?

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No! Whether a line is steep or gradual doesn't change whether it's positive or negative. A very steep downward line and a gentle downward line are both negative. Focus only on the direction.

What would a zero slope look like on this graph?

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A zero slope would be a perfectly horizontal line - completely flat with no up or down movement. It would look like a straight line parallel to the x x -axis.

Can I use the slope formula instead of just looking?

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Yes! Pick two clear points on the line and use m=y2y1x2x1 m = \frac{y_2 - y_1}{x_2 - x_1} . But for quick identification of just positive vs negative, the visual method is faster and just as reliable.

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