A number is equal to 3 times a smaller number. Also, the sum of the smaller number and 4 is the larger number. The situation is graphed on the coordinate plane below, where x represents the smaller number and y represents the larger number.

Question

On a coordinate plane, a line goes through (0, 4) and (2, 6) and another line goes through (1, 3) and (2, 6).
Which two equations represent the situation?
y = one-third x and y = x minus 4
y = one-third x and y = x + 4
y = 3 x and y = x + 4
y = 3 x and y = x minus 4

Answer 1

Let's break down the situation described in the problem step-by-step to find the two equations.

1. Identifying Relations:

   • We're given that a number \(y\) is equal to 3 times a smaller number \(x\). This gives us the equation: \[ y = 3x \]
   • We're also told that the sum of the smaller number and 4 is the larger number. This gives us a second equation: \[ y = x + 4 \]

2. Finding the Corresponding Equations:

   • The first equation we derived is \(y = 3x\).
   • The second equation we derived is \(y = x + 4\).

3. Checking Options: Now, we can confirm which option matches the equations we derived:

   • \(y = \frac{1}{3}x\) and \(y = x - 4\) (not correct)
   • \(y = \frac{1}{3}x\) and \(y = x + 4\) (not correct)
   • \(y = 3x\) and \(y = x + 4\) (correct)
   • \(y = 3x\) and \(y = x - 4\) (not correct)

Thus, the correct option is: \[ y = 3x \text{ and } y = x + 4 \]