A line has a slope of 7. For each pair of points in problems 9 to 12 that are on the line, use the slope formula to find the missing coordinate. (x, 8) and (4, 1) : (3,-6) and (7,y)

To find the missing coordinates using the slope formula, we use the formula for the slope of a line:

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

Given that the slope \( m = 7 \), we'll use this formula to solve for the missing coordinates.

### Problem 1: \( (x, 8) \) and \( (4, 1) \)

The slope is 7, and we know the points \( (x, 8) \) and \( (4, 1) \). Using the slope formula:

\[
7 = \frac{1 - 8}{4 - x}
\]

This simplifies to:

\[
7 = \frac{-7}{4 - x}
\]

Now, solve for \( x \):

\[
7(4 - x) = -7
\]

\[
28 - 7x = -7
\]

\[
28 + 7 = 7x
\]

\[
35 = 7x
\]

\[
x = 5
\]

So, the missing coordinate for the first pair is \( x = 5 \).

### Problem 2: \( (3, -6) \) and \( (7, y) \)

Again, the slope is 7, and we know the points \( (3, -6) \) and \( (7, y) \). Using the slope formula:

\[
7 = \frac{y - (-6)}{7 - 3}
\]

This simplifies to:

\[
7 = \frac{y + 6}{4}
\]

Now, solve for \( y \):

\[
7 \times 4 = y + 6
\]

\[
28 = y + 6
\]

\[
y = 28 - 6
\]

\[
y = 22
\]

So, the missing coordinate for the second pair is \( y = 22 \).

### Summary:
- For \( (x, 8) \) and \( (4, 1) \), \( x = 5 \)
- For \( (3, -6) \) and \( (7, y) \), \( y = 22 \)

Would you like further details on the solution or any clarifications? Here are 5 related questions for practice:

1. Find the slope between the points \( (2, 3) \) and \( (5, 15) \).
2. Given the points \( (0, 0) \) and \( (4, y) \), and a slope of 2, find \( y \).
3. Find the equation of the line passing through \( (2, 5) \) and \( (4, 11) \).
4. If a line has a slope of 3 and passes through \( (1, 4) \), find its equation in slope-intercept form.
5. Given two points \( (x_1, y_1) \) and \( (x_2, y_2) \), what happens to the slope if \( x_1 = x_2 \)?

**Tip:** Remember, when two points have the same x-coordinates, the slope is undefined because you cannot divide by zero!

A line has a slope of 7. For each pair of points in problems 9 to 12 that are on the line, use the slope formula to find the missing coordinate. (x, 8) and (4, 1) : (3, -6) and (7, y).

Learn how to find missing coordinates for points on a line with a slope of 7. This problem involves using the slope formula to calculate unknown values for pairs of points such as (x, 8) and (4, 1) or (3, -6) and (7, y). Suitable for students in Grades 8-10, this tutorial covers key algebraic concepts and the slope theorem.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation