Which of the following equations represents a line parallel to the line represen

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Question: Which of the following equations represents a line parallel to the line represented by 2x + 3y = 6?

Options:

Correct Answer: 2x + 3y = 12

Solution:

Parallel lines have the same slope. The equation 2x + 3y = 12 has the same slope as 2x + 3y = 6.

Which of the following equations represents a line parallel to the line represented by 2x + 3y = 6?

Which of the following equations represents a line parallel to the line represented by 2x + 3y = 6?

Step 1: Identify the given equation, which is 2x + 3y = 6.
Step 2: Rewrite the equation in slope-intercept form (y = mx + b) to find the slope. Start by isolating y.
Step 3: Subtract 2x from both sides: 3y = -2x + 6.
Step 4: Divide every term by 3 to solve for y: y = (-2/3)x + 2.
Step 5: Identify the slope (m) from the equation. The slope is -2/3.
Step 6: For a line to be parallel, it must have the same slope. So, we need to find another equation with a slope of -2/3.
Step 7: Check the options given to see which one has a slope of -2/3.

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