Math Problem Statement

What is the slope of this line?

Solution

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

m=change in ychange in x=y2y1x2x1m = \frac{{\text{{change in y}}}}{{\text{{change in x}}}} = \frac{{y_2 - y_1}}{{x_2 - x_1}}

By observing the graph, we can choose two points that the line passes through clearly:

  1. The line passes through the point (8,4)(-8, -4).
  2. The line passes through the point (4,2)(4, 2).

Now, we will calculate the slope using these two points:

m=2(4)4(8)=2+44+8=612=12m = \frac{{2 - (-4)}}{{4 - (-8)}} = \frac{{2 + 4}}{{4 + 8}} = \frac{6}{12} = \frac{1}{2}

Thus, the slope of the line is 12\frac{1}{2}.

Would you like more details on this, or do you have any questions?

Here are 5 related questions for further exploration:

  1. What is the significance of a positive slope compared to a negative slope?
  2. How would the graph change if the slope were 32\frac{3}{2}?
  3. Can you identify any other points on the line and confirm the slope calculation?
  4. What would the equation of this line be in slope-intercept form?
  5. How would you find the slope if the line were vertical or horizontal?

Tip: When identifying points on a line for calculating slope, it's best to use points where the line crosses exactly through the grid lines for more accuracy.

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Math Problem Analysis

Mathematical Concepts

Coordinate Geometry
Slope of a Line

Formulas

Slope formula: m = (y2 - y1) / (x2 - x1)

Theorems

Concept of slope

Suitable Grade Level

Grades 7-9