Question

Convert to a rectangular equation. Match each item (i)-(iv) to an item (a)-(j). Justify your answer.

1) 2x + 3y = 6
2) 3x - 4y = 12
3) 5x + 2y = 8
4) 6x - 5y = 10
5) x = 2, y = 0
6) x = 1, y = 2
7) x = 4, y = 1
8) x = 3, y = 2
9) x = 0, y = 2
10) x = 2, y = 1
11) x = 1, y = 0
12) x = 3, y = 1
13) x = 0, y = 3
14) x = 4, y = 0

Answer 1

The task is to match given points to their corresponding linear equations by substituting the x and y values into each equation. If the equation holds true with a particular set of coordinates, the point belongs to that equation. This process emphasizes the relationship between algebraic expressions and geometric representations on a graph.

Step-by-step explanation:

The student's question involves converting a set of points to a rectangular equation. A rectangular equation in two variables, x and y, represents a line in a Cartesian coordinate system. To match the points to the given equations, we need to substitute the x and y values from the points into each equation and determine which one holds true. Let's illustrate this with an example:

• For the point (2, 0), substituting into equation 1) 2x + 3y = 6, we get 2(2) + 3(0) = 4, which does not equal 6. Thus, this point does not match equation 1).
• For equation 2) 3x - 4y = 12 and the point (4, 0), substituting we get 3(4) - 4(0) = 12, which satisfies the equation, so the point (4, 0) matches equation 2).

By performing this process for each point with each equation, the student can determine which points correspond to which linear equations. Each solution provides a specific example of how the variables are interrelated in a clear and concise manner. This exercise strengthens understanding of fundamental algebraic concepts such as solving equations and graphing lines.