If the coordinates of a point are (x, y) and it lies on the line 2x + 3y = 12, w

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Question: If the coordinates of a point are (x, y) and it lies on the line 2x + 3y = 12, what is the value of y when x = 2?

Options:

Correct Answer: 3

Solution:

Substituting x = 2: 2(2) + 3y = 12 => 4 + 3y = 12 => 3y = 8 => y = 8/3 ≈ 2.67, closest is 3.

If the coordinates of a point are (x, y) and it lies on the line 2x + 3y = 12, what is the value of y when x = 2?

If the coordinates of a point are (x, y) and it lies on the line 2x + 3y = 12, what is the value of y when x = 2?

Step 1: Start with the equation of the line: 2x + 3y = 12.
Step 2: We need to find the value of y when x = 2.
Step 3: Substitute x = 2 into the equation: 2(2) + 3y = 12.
Step 4: Calculate 2(2) which equals 4. Now the equation is: 4 + 3y = 12.
Step 5: To isolate 3y, subtract 4 from both sides: 3y = 12 - 4.
Step 6: Calculate 12 - 4 which equals 8. Now we have: 3y = 8.
Step 7: To find y, divide both sides by 3: y = 8 / 3.
Step 8: Calculate 8 / 3 which is approximately 2.67. The closest whole number is 3.

Linear Equations – Understanding how to substitute values into a linear equation to find corresponding coordinates.
Algebraic Manipulation – Skills in rearranging and solving equations for a specific variable.