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

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": 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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