What is the slope of the line that passes through the points left parenthesis, 8, comma, minus, 6, right parenthesis(8,−6) and left parenthesis, 5, comma, minus, 1, right parenthesis(5,−1)? Write your answer in simplest form.

To find the slope of the line that passes through the points \((8, -6)\) and \((5, -1)\), we use the slope formula:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Here, \((x_1, y_1) = (8, -6)\) and \((x_2, y_2) = (5, -1)\).

Substituting the coordinates into the slope formula:

\[
m = \frac{-1 - (-6)}{5 - 8}
\]

Simplify the expression:

\[
m = \frac{-1 + 6}{5 - 8} = \frac{5}{-3} = -\frac{5}{3}
\]

So, the slope of the line is \(\boxed{-\frac{5}{3}}\).

Would you like any further details or explanations? Here are some related questions you might find helpful:

1. How do you interpret the slope of a line in real-world scenarios?
2. How do you find the equation of a line given two points?
3. What does a negative slope indicate about the direction of a line?
4. How can you verify the slope calculation by graphing the points?
5. How does the slope relate to the angle of a line with the x-axis?

**Tip:** Always remember that the slope of a line represents how much the y-coordinate changes for a unit change in the x-coordinate.

What is the slope of the line that passes through the points (8,−6) and (5,−1)? Write your answer in simplest form.

Learn how to calculate the slope of a line passing through the points (8,−6) and (5,−1) using the slope formula. This detailed solution is perfect for students in Grades 8-10 and covers key algebraic concepts such as linear equations and slope calculation.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation