The equation of a line parallel to y = 2x + 3 and passing through (1, 1) is?

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Question: The equation of a line parallel to y = 2x + 3 and passing through (1, 1) is?

Options:

Correct Answer: y = 2x - 1

Solution:

Parallel lines have the same slope. Using point-slope form: y - 1 = 2(x - 1) => y = 2x - 1.

The equation of a line parallel to y = 2x + 3 and passing through (1, 1) is?

The equation of a line parallel to y = 2x + 3 and passing through (1, 1) is?

Step 1: Identify the slope of the given line y = 2x + 3. The slope (m) is 2.
Step 2: Since parallel lines have the same slope, the slope of the new line will also be 2.
Step 3: Use the point-slope form of a line equation, which is y - y1 = m(x - x1). Here, (x1, y1) is the point (1, 1) and m is 2.
Step 4: Substitute the values into the point-slope form: y - 1 = 2(x - 1).
Step 5: Simplify the equation: y - 1 = 2x - 2.
Step 6: Add 1 to both sides to solve for y: y = 2x - 1.

Slope of a Line – Understanding that parallel lines share the same slope.
Point-Slope Form – Using the point-slope form of a line equation to find the equation of a line given a point and slope.