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Slope

Grades 7-9 · Concept Explainer

Key Points

  • ✓Slope is a measure of steepness.
  • ✓Slope is rise over run (vertical change divided by horizontal change).
  • ✓Positive slope means the line goes up from left to right.
  • ✓Negative slope means the line goes down from left to right.
  • ✓A horizontal line has a slope of 0.
  • ✓A vertical line has an undefined slope.

Slope is a way to describe how steep a line is. It tells you how much the line goes up or down for every step you take to the right. A positive slope means the line goes uphill, while a negative slope means it goes downhill. A slope of zero means the line is flat (horizontal). The steeper the line, the bigger the number (positive or negative) representing the slope.

Worked Example

Find the slope of a line that passes through the points (1, 2) and (4, 8).

  1. Step 1: Identify the coordinates of the two points: (x1, y1) = (1, 2) and (x2, y2) = (4, 8).
  2. Step 2: Use the slope formula: slope = (y2 - y1) / (x2 - x1).
  3. Step 3: Plug in the values: slope = (8 - 2) / (4 - 1).
  4. Step 4: Simplify: slope = 6 / 3.
  5. Step 5: Calculate the slope: slope = 2.

Answer: The slope is 2.

Try It Yourself

1. What is the slope of a line that passes through the points (0, 0) and (2, 4)?

2. A line has a slope of -1/2 and passes through the point (2, 3). What is the y-coordinate of the point on the line where x = 4?

3. Line A passes through (1,5) and (4,11). Line B is perpendicular to Line A and passes through the point (2,3). What is the equation of Line B in slope-intercept form?

Watch Out For These Mistakes

  • Forgetting to use the correct order when subtracting coordinates in the slope formula (y2 - y1) / (x2 - x1).
  • Confusing rise and run (switching the numerator and denominator).
  • Not understanding the difference between positive and negative slopes.
  • Thinking a vertical line has a slope of 0.