If a line passes through the points (1, 1) and (2, 3), what is its equation in slope-intercept form?
Correct Answer: y = 2x - 1
- Step 1: Identify the two points given: (1, 1) and (2, 3).
- Step 2: Use the formula for slope (m) which is (y2 - y1) / (x2 - x1). Here, y2 = 3, y1 = 1, x2 = 2, and x1 = 1.
- Step 3: Substitute the values into the slope formula: m = (3 - 1) / (2 - 1).
- Step 4: Calculate the slope: m = 2 / 1 = 2.
- Step 5: Now, use the point-slope form of the equation: y - y1 = m(x - x1). Here, use point (1, 1) and slope m = 2.
- Step 6: Substitute the values into the point-slope form: y - 1 = 2(x - 1).
- Step 7: Simplify the equation: y - 1 = 2x - 2.
- Step 8: Add 1 to both sides to solve for y: y = 2x - 2 + 1.
- Step 9: Finalize the equation: y = 2x - 1.
- Slope Calculation – Understanding how to calculate the slope (m) 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.
- Slope-Intercept Form – Converting the equation from point-slope form to slope-intercept form (y = mx + b).
