Final answer:
The equation of the line passing through the points (3,3) and (4,6) is found by first calculating the slope and then using the point-slope form. The final equation of the line is y = 3x - 3.
Step-by-step explanation:
To write an equation of a line that passes through the points (3,3) and (4,6), you need to find the slope of the line first. The slope, m, is found using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.
Using the given points, the slope is m = (6 - 3) / (4 - 3) = 3 / 1 = 3. Now that we have the slope, we can use the point-slope form of a line which is y - y1 = m(x - x1). Plugging in the slope we found and one of the points, for example (3,3), we get the equation of the line: y - 3 = 3(x - 3). Simplifying this, we get y = 3x - 6 + 3, which simplifies further to y = 3x - 3.
Therefore, the equation of the line that passes through the points (3,3) and (4,6) is y = 3x - 3.