Math Problem Statement

What is the slope of the line passing through the points (0, -3) and (4, 5)?

Solution

The graph provided shows two labeled points: (0,3)(0, -3) and (4,5)(4, 5).

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

m=y2y1x2x1m = \frac{y_2 - y_1}{x_2 - x_1}

Where:

  • (x1,y1)=(0,3)(x_1, y_1) = (0, -3)
  • (x2,y2)=(4,5)(x_2, y_2) = (4, 5)

Substitute the values:

m=5(3)40=5+34=84=2m = \frac{5 - (-3)}{4 - 0} = \frac{5 + 3}{4} = \frac{8}{4} = 2

So, the slope of the line is 22.

Would you like further details or have any questions?

Here are 5 related questions to explore:

  1. How do you find the equation of a line given its slope and a point?
  2. What is the interpretation of slope in real-world scenarios?
  3. How does a negative slope affect the direction of a line?
  4. Can the slope of a vertical line be calculated? Why or why not?
  5. How does the slope relate to the angle of a line with respect to the x-axis?

Tip: When calculating slope, make sure to correctly subtract the coordinates to avoid errors!

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Math Problem Analysis

Mathematical Concepts

Algebra
Coordinate Geometry
Slope of a Line

Formulas

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

Theorems

Concept of slope in linear equations

Suitable Grade Level

Grades 8-10