Final answer:
The equation of the line passing through the points (1, 1) and (3, 9) is y = 4x - 3.
Step-by-step explanation:
The equation of the line passing through the points (1, 1) and (3, 9) can be found by first calculating the slope and then using the y-intercept to write the equation in y=mx+b format.
Step 1: Finding the Slope
The slope of a line is given by the formula: m = (y2 - y1) / (x2 - x1). Substituting the coordinates of the two points, we get: m = (9 - 1) / (3 - 1) = 8 / 2 = 4.
Step 2: Finding the Y-Intercept
The y-intercept is the value of y when x=0. To find it, we can plug one of the given points into the equation and solve for b. Using (1, 1), we get: 1 = 4(1) + b which simplifies to b = 1 - 4 = -3.
Step 3: Writing the Equation
Now that we have the slope (m = 4) and the y-intercept (b = -3), we can write the equation in y=mx+b form: y = 4x - 3.