Final answer:
The equation of the line that passes through the points (2, 6) and (0, 3) is found by calculating the slope, which is 1.5, and then using one of the points to find the y-intercept, which is 3. This gives us the final equation y = 1.5x + 3.
Step-by-step explanation:
To find the equation of a line that passes through two points, we first need to find the slope (m) and then use one of the points to solve for the y-intercept (b) in the slope-intercept form of a line, which is y = mx + b.
Finding the Slope
The slope can be found using the formula m = (y2 - y1) / (x2 - x1). For the points (2, 6) and (0, 3), the slope would be (6 - 3) / (2 - 0) = 3 / 2. Therefore, the slope is 1.5.
Finding the Y-Intercept
Next, we plug in the slope and one of the points into the equation y = mx + b to find the y-intercept.
Using the point (0, 3):
3 = (1.5)(0) + b
b = 3
Final Equation
Finally, the equation of the line is y = 1.5x + 3.