If two lines are parallel and one line has the equation y = 3x + 2, what is the
Practice Questions
Q1
If two lines are parallel and one line has the equation y = 3x + 2, what is the equation of a line parallel to it that passes through the point (1, 4)?
y = 3x + 1
y = 3x + 4
y = 3x + 2
y = 3x - 1
Questions & Step-by-Step Solutions
If two lines are parallel and one line has the equation y = 3x + 2, what is the equation of a line parallel to it that passes through the point (1, 4)?
Step 1: Identify the slope of the given line. The equation is y = 3x + 2, so the slope (m) is 3.
Step 2: Understand that parallel lines have the same slope. Therefore, the slope of the new line will also be 3.
Step 3: Use the point-slope form of a line's equation, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line.
Step 4: Substitute the point (1, 4) into the point-slope form. Here, x1 = 1, y1 = 4, and m = 3.
Step 5: Write the equation: y - 4 = 3(x - 1).
Step 6: Simplify the equation. Distribute 3: y - 4 = 3x - 3.
Step 7: Add 4 to both sides to solve for y: y = 3x + 1.
