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

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

Options:

Correct Answer: y = 2x + 1

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 that passes through the points (2, 3) and (4, 7).

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

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: Substitute the values into the slope formula: m = (7 - 3) / (4 - 2).
Step 4: Calculate the slope: m = 4 / 2 = 2.
Step 5: Use the point-slope form of the equation: y - y1 = m(x - x1). Choose one of the points, for example (2, 3).
Step 6: Substitute the slope and the point into the equation: y - 3 = 2(x - 2).
Step 7: Simplify the equation: y - 3 = 2x - 4.
Step 8: Add 3 to both sides to solve for y: y = 2x - 4 + 3.
Step 9: Finalize the equation: y = 2x - 1.

Slope Calculation – Understanding how to calculate the slope between two points using the formula m = (y2 - y1) / (x2 - x1).
Point-Slope Form – Using the point-slope form of a line, y - y1 = m(x - x1), to derive the equation of the line.
Equation of a Line – Converting the point-slope form to slope-intercept form (y = mx + b) to express the line's equation.