Math Problem Statement

Answer

Find the slope of the line graphed below.

Solution

To find the slope of the line from the graph, we can use the slope formula m=y2y1x2x1m = \frac{{y_2 - y_1}}{{x_2 - x_1}}. This formula calculates the change in yy (rise) over the change in xx (run) between two points on the line.

Looking at the graph, it appears that the line passes through the points (2,1)(2, 1) and (4,4)(4, 4). Using these points:

  1. x1=2x_1 = 2, y1=1y_1 = 1
  2. x2=4x_2 = 4, y2=4y_2 = 4

Now, applying the slope formula:

m=4142=32m = \frac{{4 - 1}}{{4 - 2}} = \frac{3}{2}

So, the slope of the line is 32\frac{3}{2}.

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

Here are 5 related questions:

  1. What is the general formula for the slope of a line?
  2. How do you find the slope if the graph has negative coordinates?
  3. What happens to the slope if the line is horizontal or vertical?
  4. How does slope relate to the equation of a line in slope-intercept form?
  5. How would you find the slope of a curved line at a specific point?

Tip: To check your slope visually, look at the rise and run between any two points on the line!

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Slope

Formulas

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

Theorems

Slope of a line

Suitable Grade Level

Grades 8-10