Select the correct answer from each drop-down menu.
The slope of the line passing through the points (7, 5) and (21, 15) is ?
.

Another line with a slope that is one-third that of the slope you just calculated passes through the origin and the point ?
.

Let's first calculate the slope of the line passing through the points (7, 5) and (21, 15).

The formula for the slope (\( m \)) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Substituting the given points \((7, 5)\) and \((21, 15)\):
\[
m = \frac{15 - 5}{21 - 7} = \frac{10}{14} = \frac{5}{7}
\]

The slope of the line passing through the points (7, 5) and (21, 15) is \( \frac{5}{7} \).

Now, we need to find the slope of another line that is one-third of the slope we just calculated:
\[
\text{New slope} = \frac{1}{3} \times \frac{5}{7} = \frac{5}{21}
\]

This new line passes through the origin (0, 0). To find another point on this line, we can use the slope formula again. For simplicity, let’s use the point-slope form of the line equation, which is:
\[
y = mx
\]

Substituting the new slope:
\[
y = \frac{5}{21}x
\]

Let's choose \( x = 21 \) to find a point on the line:
\[
y = \frac{5}{21} \times 21 = 5
\]

So, the point is (21, 5).

Therefore, the answers are:

The slope of the line passing through the points (7, 5) and (21, 15) is \( \frac{5}{7} \).

Another line with a slope that is one-third that of the slope you just calculated passes through the origin and the point (21, 5).

Would you like more details or have any questions? Here are 5 questions you might consider asking next:

1. How do you find the equation of a line given two points?
2. What is the significance of the slope in a linear equation?
3. How do you interpret the slope of a line in a real-world context?
4. Can you explain how to determine if two lines are parallel or perpendicular?
5. How do you use the point-slope form to write the equation of a line?

Tip: When working with slopes, ensure to simplify fractions to their lowest terms for clarity and accuracy.

Learn how to calculate the slope of a line passing through given points and find another line with one-third of that slope. This problem covers coordinate geometry concepts and formulas for slopes and line equations. Suitable for students in Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation