Math Problem Statement

Answer

Multiple math questions involving solving linear equations, determining slopes, interpreting graphs, and applying algebraic formulas.

Solution

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

10. What is the value of y in the equation xy=4x - y = 4 given that x=8x = 8?

  • 8y=4y=84=48 - y = 4 \Rightarrow y = 8 - 4 = 4 Answer: D. 4

11. Which equation below satisfies the ordered pair (-2, -7)?

  • A. 2y=x+172y = x + 17: 2(7)=2+1714152(-7) = -2 + 17 \Rightarrow -14 \neq 15
  • B. 11xy=1511x - y = -15: 11(2)(7)=1522+7=1511(-2) - (-7) = -15 \Rightarrow -22 + 7 = -15 Answer: B. 11x - y = -15

12. In the equation 2x+3y=72x + 3y = 7, when y=1y = 1, what would be the corresponding value of xx?

  • 2x+3(1)=72x+3=72x=4x=22x + 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=y2y1x2x1m = \frac{y_2 - y_1}{x_2 - x_1}
  • m=3338=0m = \frac{3 - 3}{-3 - 8} = 0 Answer: A. 0

16. Determine the slope of the equation 8x12y=68x - 12y = 6.

  • Rewrite in slope-intercept form: 12y=8x6y=812x612=23x1212y = 8x - 6 \Rightarrow y = \frac{8}{12}x - \frac{6}{12} = \frac{2}{3}x - \frac{1}{2} Answer: A. 23\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=10532=51=5m = \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=3004=34=34m = \frac{-3 - 0}{0 - 4} = \frac{-3}{-4} = \frac{3}{4} Answer: C. 34\frac{3}{4}

19. Determine the slope and y-intercept of the line 2x=y+42x = y + 4.

  • Rewrite as y=2x4y = 2x - 4, so slope m=2m = 2 and y-intercept b=4b = -4. Answer: B. m=2;b=4m = 2; b = -4

20. In the equation 6x+y=26x + y = 2, what is the slope?

  • Rewrite as y=6x+2y = -6x + 2, so slope m=6m = -6. Answer: D. -6

21. Which of the following statements is correct about the two given linear equations?

  1. 3x6y=153x - 6y = 15y=12x52y = \frac{1}{2}x - \frac{5}{2} (slope 12\frac{1}{2})
  2. 8x4y=128x - 4y = 12y=2x3y = 2x - 3 (slope 22) 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 xx number of sessions?

  • The equation is y=25x+120y = 25x + 120. **Answer: A. (y

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Math Problem Analysis

Mathematical Concepts

Linear Equations
Slope of a Line
Graph Interpretation
Algebraic Manipulation

Formulas

Slope Formula: m = (y2 - y1) / (x2 - x1)
Linear Equation: y = mx + b
Rewriting equations into slope-intercept form
Solving systems of linear equations

Theorems

Slope-Intercept Theorem
Line Equation Theorem
Graphing Linear Equations

Suitable Grade Level

Grades 8-10