Find the equation of the line passing through the points (1, 2) and (3, 4).

Find the equation of the line passing through the points (1, 2) and (3, 4).

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