Question

Line p is defined by the equation \(2y + 3x = 6\).
Quantity A: The y-intercept of line p.
Quantity B: The x-intercept of line p.

• A. if Quantity A is greater;
• B. if Quantity B is greater;
• C. if the two quantities are equal;
• D. if the relationship cannot be determined from the information given.
• E.

Hint:

A quick way to find intercepts from the standard form \(Ax + By = C\) is to use the "cover-up" method. To find the y-intercept, cover the x-term (\(3x\)) and solve \(2y = 6\), which gives \(y = 3\). To find the x-intercept, cover the y-term (\(2y\)) and solve \(3x = 6\), which gives \(x = 2\).

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
The question asks us to compare the x- and y-intercepts of a given line. The y-intercept is the point where the line crosses the y-axis (where \(x=0\)). The x-intercept is the point where the line crosses the x-axis (where \(y=0\)).
Step 2: Key Formula or Approach:
The equation of the line is \(2y + 3x = 6\).
To find the y-intercept, we set \(x = 0\) and solve for \(y\).
To find the x-intercept, we set \(y = 0\) and solve for \(x\).
Step 3: Detailed Explanation:
Calculate Quantity A (The y-intercept):
Set \(x = 0\) in the equation \(2y + 3x = 6\): \[ 2y + 3(0) = 6 \] \[ 2y = 6 \] \[ y = 3 \] So, the y-intercept is 3. Quantity A = 3.
Calculate Quantity B (The x-intercept):
Set \(y = 0\) in the equation \(2y + 3x = 6\): \[ 2(0) + 3x = 6 \] \[ 3x = 6 \] \[ x = 2 \] So, the x-intercept is 2. Quantity B = 2.
Step 4: Final Answer:
Now we compare the two quantities:
Quantity A = 3
Quantity B = 2
Since \(3 \textgreater 2\), Quantity A is greater than Quantity B.