https://file.aiquickdraw.com/mathbot/file/1727269302903z84zzvh4.jpg

Let's go through and solve the questions step by step:

### 10. What is the value of y in the equation \(x - y = 4\) given that \(x = 8\)?
- \(8 - y = 4 \Rightarrow y = 8 - 4 = 4\)
  **Answer: D. 4**

### 11. Which equation below satisfies the ordered pair (-2, -7)?
- A. \(2y = x + 17\): \(2(-7) = -2 + 17 \Rightarrow -14 \neq 15\)
- B. \(11x - y = -15\): \(11(-2) - (-7) = -15 \Rightarrow -22 + 7 = -15 \)
  **Answer: B. 11x - y = -15**

### 12. In the equation \(2x + 3y = 7\), when \(y = 1\), what would be the corresponding value of \(x\)?
- \(2x + 3(1) = 7 \Rightarrow 2x + 3 = 7 \Rightarrow 2x = 4 \Rightarrow x = 2\)
  **Answer: B. 2**

### 13. Which of the following statements does **NOT** describe a slope?
- A. It can be found using a graph (True).
- B. It can be determined using a point (True).
- C. It is referred to as the rise over run (True).
- D. It describes the steepness of a line (True).
  **Answer: B. It can be determined using a point** (as slope typically uses two points).

### 14. What is the slope of a line that has coordinates (5,18) and (5,-12)?
- Since the x-coordinates are the same, this is a vertical line, and the slope is undefined.
  **Answer: C. undefined**

### 15. Determine the slope of a line that passes through the points (8,3) and (-3,3).
- Slope formula: \(m = \frac{y_2 - y_1}{x_2 - x_1}\)
- \(m = \frac{3 - 3}{-3 - 8} = 0\)
  **Answer: A. 0**

### 16. Determine the slope of the equation \(8x - 12y = 6\).
- Rewrite in slope-intercept form: \(12y = 8x - 6 \Rightarrow y = \frac{8}{12}x - \frac{6}{12} = \frac{2}{3}x - \frac{1}{2}\)
  **Answer: A. \(\frac{2}{3}\)**

### 17. Which of the following pair of points has a slope of 5?
- Using the slope formula on each pair:
  - A. \(m = \frac{10 - 5}{3 - 2} = \frac{5}{1} = 5\)
  **Answer: A. (2,5) and (3,10)**

### 18. What is the slope of the line on the graph at the right?
- The slope can be calculated using points from the graph.
  \(m = \frac{-3 - 0}{0 - 4} = \frac{-3}{-4} = \frac{3}{4}\)
  **Answer: C. \(\frac{3}{4}\)**

### 19. Determine the slope and y-intercept of the line \(2x = y + 4\).
- Rewrite as \(y = 2x - 4\), so slope \(m = 2\) and y-intercept \(b = -4\).
  **Answer: B. \(m = 2; b = -4\)**

### 20. In the equation \(6x + y = 2\), what is the slope?
- Rewrite as \(y = -6x + 2\), so slope \(m = -6\).
  **Answer: D. -6**

### 21. Which of the following statements is correct about the two given linear equations?
  1. \(3x - 6y = 15\) → \(y = \frac{1}{2}x - \frac{5}{2}\) (slope \(\frac{1}{2}\))
  2. \(8x - 4y = 12\) → \(y = 2x - 3\) (slope \(2\))
  **Answer: D. The slope of equation 1 is less than the slope of equation 2.**

### 22. Ana decided to join a Zumba session. The initial fee is Php 120, and a Php 25 fee for each session. Which of the following equations model the amount your sister will pay in \(x\) number of sessions?
- The equation is \(y = 25x + 120\).
  **Answer: A. \(y

Solve the following math problems related to algebra, slopes, and linear equations.

Step-by-step solutions to algebra and coordinate geometry problems involving linear equations, slope calculation, and intercepts. Suitable for students in Grades 8-10, this lesson covers concepts such as slope determination, equation solving, and interpretation of graphs.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation