Find the equation of the line parallel to y = 5x - 2 that passes through the poi

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Question: Find the equation of the line parallel to y = 5x - 2 that passes through the point (2, 3).

Options:

Correct Answer: y = 5x - 7

Solution:

Since the slope is the same (5), using point-slope form: y - 3 = 5(x - 2) gives y = 5x - 7.

Find the equation of the line parallel to y = 5x - 2 that passes through the point (2, 3).

Find the equation of the line parallel to y = 5x - 2 that passes through the point (2, 3).

Step 1: Identify the slope of the given line y = 5x - 2. The slope (m) is 5.
Step 2: Since we need a line parallel to this one, it will have the same slope, which is 5.
Step 3: Use the point-slope form of the equation of a line, which is y - y1 = m(x - x1). Here, (x1, y1) is the point (2, 3).
Step 4: Substitute the values into the point-slope form: y - 3 = 5(x - 2).
Step 5: Simplify the equation. Distribute 5: y - 3 = 5x - 10.
Step 6: Add 3 to both sides to solve for y: y = 5x - 10 + 3.
Step 7: Combine like terms: y = 5x - 7.
Step 8: The final equation of the line parallel to y = 5x - 2 that passes through (2, 3) is y = 5x - 7.

Slope of a Line – Understanding that parallel lines have 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.
Equation of a Line – Converting from point-slope form to slope-intercept form.