Math Problem Statement

What is the slope of the line that passes through the points (4, -6) and (-2, 3)? Write your answer in simplest form.

Solution

To solve for the slope of the line passing through the points (4,6)(4, -6) and (2,3)(-2, 3), we use the slope formula:

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

Step-by-Step Solution:

  1. Assign the coordinates:

    • (x1,y1)=(4,6)(x_1, y_1) = (4, -6)
    • (x2,y2)=(2,3)(x_2, y_2) = (-2, 3)
  2. Substitute into the formula: m=3(6)24m = \frac{3 - (-6)}{-2 - 4}

  3. Simplify:

    • Numerator: 3(6)=3+6=93 - (-6) = 3 + 6 = 9
    • Denominator: 24=6-2 - 4 = -6

    m=96m = \frac{9}{-6}

  4. Simplify further: m=32m = -\frac{3}{2}

Final Answer:

The slope of the line is: m=32m = -\frac{3}{2}

Would you like more details or have questions? Here are five follow-up concepts:

  1. What does a slope of 32-\frac{3}{2} indicate about the line's direction?
  2. How do we interpret slope in the context of rise over run?
  3. Can you find the equation of this line in slope-intercept form?
  4. How do we verify the slope using the distance formula?
  5. What happens to the slope if the two points are swapped?

Tip: Always simplify fractions in slope calculations to avoid errors!

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Algebra
Analytic Geometry
Linear Equations

Formulas

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

Theorems

-

Suitable Grade Level

Grades 8-10