Math Problem Statement

Find the slope of the line graphed below.

Solution

To find the slope of the line in the graph, we use the formula for slope:

slope=y2y1x2x1\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}

From the image, I can identify two points on the line:

  1. Point 1: (4,0)(-4, 0)
  2. Point 2: (4,3)(4, 3)

Now, using these coordinates in the slope formula:

slope=304(4)=34+4=38\text{slope} = \frac{3 - 0}{4 - (-4)} = \frac{3}{4 + 4} = \frac{3}{8}

So, the slope of the line is 38\frac{3}{8}.

Would you like more details or have any questions? Here are 5 related questions you might find helpful:

  1. How does the slope of a line affect its steepness?
  2. What does a positive slope signify about the direction of a line?
  3. Can a line have a slope of zero? What would that look like?
  4. What happens when the slope is negative?
  5. How do we find the equation of a line once we know its slope and a point?

Tip: The slope of a line tells you how much the yy-coordinate changes for every unit change in the xx-coordinate!

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Math Problem Analysis

Mathematical Concepts

Coordinate Geometry
Linear Equations
Slope Calculation

Formulas

Slope = (y2 - y1) / (x2 - x1)

Theorems

Slope formula in coordinate geometry

Suitable Grade Level

Grades 6-8