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

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

Options:

Correct Answer: y = 2x

Solution:

Slope = (6-2)/(3-1) = 2. Using point-slope form: y - 2 = 2(x - 1) gives y = 2x.

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

What is the equation of a line that passes 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: Slope (m) = (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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