Math Problem Statement

What is the slope of the line?

Solution

To find the slope of the line, we use the slope formula, which is:

slope=ΔyΔx=y2y1x2x1\text{slope} = \frac{{\Delta y}}{{\Delta x}} = \frac{{y_2 - y_1}}{{x_2 - x_1}}

From the graph, we can pick two points where the line crosses the grid. The two points are:

  • Point 1: (3,1)(-3, -1)
  • Point 2: (2,2)(2, 2)

Now, applying the slope formula:

slope=2(1)2(3)=2+12+3=35\text{slope} = \frac{{2 - (-1)}}{{2 - (-3)}} = \frac{{2 + 1}}{{2 + 3}} = \frac{3}{5}

So, the slope of the line is:

35\boxed{\frac{3}{5}}

Would you like further details or have any questions?

Here are 5 related questions:

  1. How would you find the equation of the line from this slope?
  2. What is the y-intercept of the line in this graph?
  3. How do parallel lines relate in terms of slope?
  4. What does a negative slope indicate on a graph?
  5. How do you determine the slope if the points are fractional?

Tip: When reading a graph, always choose points where the line crosses the grid cleanly for accurate calculations.

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Math Problem Analysis

Mathematical Concepts

Algebra
Slope of a Line
Graph Interpretation

Formulas

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

Theorems

Slope-Intercept Theorem

Suitable Grade Level

Grades 7-9