Find the equation of the line passing through the points (2, 3) and (4, 7). (202

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Question: Find the equation of the line passing through the points (2, 3) and (4, 7). (2020)

Options:

Correct Answer: y = 2x + 1

Exam Year: 2020

Solution:

The slope m = (7 - 3) / (4 - 2) = 2. Using point-slope form: y - 3 = 2(x - 2) gives y = 2x + 1.

Find the equation of the line passing through the points (2, 3) and (4, 7). (2020)

Find the equation of the line passing through the points (2, 3) and (4, 7). (2020)

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

Slope Calculation – Understanding how to calculate the slope of a line given two points.
Point-Slope Form – Using the point-slope form of a linear equation to derive the equation of a line.
Linear Equation – Converting the point-slope form to slope-intercept form (y = mx + b).