Calculate the exact slope m (rather than a decimal approximation) of the straight line through the given pair of points, if defined. Try to do the problem without writing anything down except the answer. (If an answer is undefined, enter UNDEFINED.)
(0, 1) and

−
1
6
,
7
8

To find the slope \( m \) of a line passing through two points, we use the formula for slope:

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

Given points are \((0, 1)\) and \(\left( -\frac{1}{6}, \frac{7}{8} \right)\).

Substitute these values into the formula:

\[
m = \frac{\frac{7}{8} - 1}{-\frac{1}{6} - 0}
\]

First, simplify the numerator:

\[
\frac{7}{8} - 1 = \frac{7}{8} - \frac{8}{8} = -\frac{1}{8}
\]

Now simplify the denominator:

\[
-\frac{1}{6} - 0 = -\frac{1}{6}
\]

Now divide the two fractions:

\[
m = \frac{-\frac{1}{8}}{-\frac{1}{6}} = \frac{1}{8} \times \frac{6}{1} = \frac{6}{8} = \frac{3}{4}
\]

Thus, the slope \( m \) is:

\[
m = \frac{3}{4}
\]

Let me know if you want more details or have any questions.

Here are five related questions:
1. How do you find the slope if one of the points is the origin?
2. What happens to the slope if the x-coordinates of both points are the same?
3. Can two points on a vertical line have a defined slope?
4. How does changing the order of points affect the slope calculation?
5. What is the significance of a slope of 0?

**Tip:** The slope formula is a ratio, so understanding fractions simplifies slope calculations.

Calculate the exact slope m (rather than a decimal approximation) of the straight line through the given pair of points, if defined. Try to do the problem without writing anything down except the answer. (If an answer is undefined, enter UNDEFINED.) (0, 1) and (-1/6, 7/8)

Learn how to calculate the exact slope of a straight line passing through the points (0, 1) and (-1/6, 7/8) using the slope formula. This guide includes a step-by-step breakdown of the process, including simplifying fractions. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation