If the line 3x - 4y + 12 = 0 is parallel to which of the following lines?

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Question: If the line 3x - 4y + 12 = 0 is parallel to which of the following lines?

Options:

Correct Answer: 6x - 8y + 24 = 0

Solution:

Parallel lines have the same slope. The slope of the given line is 3/4, which is the same as the slope of 6x - 8y + 24 = 0.

If the line 3x - 4y + 12 = 0 is parallel to which of the following lines?

If the line 3x - 4y + 12 = 0 is parallel to which of the following lines?

Step 1: Identify the equation of the given line, which is 3x - 4y + 12 = 0.
Step 2: Rearrange the equation into slope-intercept form (y = mx + b) to find the slope.
Step 3: Start by isolating y: 3x - 4y + 12 = 0 becomes -4y = -3x - 12.
Step 4: Divide every term by -4 to solve for y: y = (3/4)x + 3.
Step 5: Identify the slope (m) from the equation, which is 3/4.
Step 6: Understand that parallel lines have the same slope.
Step 7: Check the other line options to find one with the same slope of 3/4.
Step 8: Rearrange the equation of the other line (6x - 8y + 24 = 0) into slope-intercept form.
Step 9: Isolate y: 6x - 8y + 24 = 0 becomes -8y = -6x - 24.
Step 10: Divide every term by -8 to solve for y: y = (3/4)x + 3.
Step 11: Confirm that the slope of this line is also 3/4, meaning it is parallel to the original line.

Slope of a Line – Understanding that parallel lines have the same slope, which can be derived from the standard form of a linear equation.
Standard Form of a Line – Recognizing how to convert the standard form of a line (Ax + By + C = 0) to slope-intercept form (y = mx + b) to find the slope.