The equation of a line passing through the points (1, 2) and (3, 6) is:

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

Options:

Correct Answer: y = 2x

Solution:

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

The equation of a line passing through the points (1, 2) and (3, 6) is:

The equation of a line passing through the points (1, 2) and (3, 6) is:

Step 1: Identify the two points given: (1, 2) and (3, 6).
Step 2: Use the formula for slope, which is (y2 - y1) / (x2 - x1). Here, y2 = 6, y1 = 2, x2 = 3, and x1 = 1.
Step 3: Substitute the values into the slope formula: (6 - 2) / (3 - 1).
Step 4: Calculate the difference in y-coordinates: 6 - 2 = 4.
Step 5: Calculate the difference in x-coordinates: 3 - 1 = 2.
Step 6: Now divide the difference in y by the difference in x: 4 / 2 = 2. This is the slope of the line.
Step 7: Use the point-slope form of the equation: y - y1 = m(x - x1), where m is the slope and (x1, y1) is one of the points.
Step 8: Substitute the slope (2) and the point (1, 2) into the equation: y - 2 = 2(x - 1).
Step 9: Simplify the equation: y - 2 = 2x - 2.
Step 10: Add 2 to both sides to solve for y: y = 2x.

Slope Calculation – Understanding how to calculate the slope of a line using two points.
Point-Slope Form – Using the point-slope form of a linear equation to derive the equation of a line.
Linear Equation – Recognizing the standard form of a linear equation and how to manipulate it.