What is the equation of the line passing through the points (1, 2) and (3, 6)?

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Question: What is the equation of the line passing through the points (1, 2) and (3, 6)?

Options:

Correct Answer: y = 2x

Solution:

The slope m = (6 - 2) / (3 - 1) = 2. Using point-slope form, y - 2 = 2(x - 1) gives y = 2x.

What is the equation of the line passing through the points (1, 2) and (3, 6)?

What is the equation of the line passing through the points (1, 2) and (3, 6)?

Step 1: Identify the two points given: (1, 2) and (3, 6).
Step 2: Use the formula for slope (m) which is (y2 - y1) / (x2 - x1). Here, (x1, y1) = (1, 2) and (x2, y2) = (3, 6).
Step 3: Substitute the values into the slope formula: m = (6 - 2) / (3 - 1).
Step 4: Calculate the slope: m = 4 / 2 = 2.
Step 5: Use the point-slope form of the equation: y - y1 = m(x - x1). Here, use point (1, 2) and slope m = 2.
Step 6: Substitute the values into the point-slope form: y - 2 = 2(x - 1).
Step 7: Simplify the equation: y - 2 = 2x - 2.
Step 8: Add 2 to both sides to solve for y: y = 2x.

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