Final answer:
To find the equation of the line that passes through the given points, we can use the slope-intercept form of a linear equation, y = mx + b. By calculating the slope and plugging it into the equation, we can determine the equation of the line.
Step-by-step explanation:
To find the equation of the line that passes through the points A (0, 0), B (2, 3), C (4, 6), and D (8, 12), we can use the slope-intercept form of a linear equation, y = mx + b. First, we need to find the slope of the line using the formula: m = (y2 - y1) / (x2 - x1). Let's calculate the slope:
m = (3 - 0) / (2 - 0) = 3/2.
Now that we have the slope, we can plug it into the equation y = mx + b using any of the given points. Let's use point A (0, 0):
0 = (3/2)(0) + b.
Simplifying the equation, we find that b = 0. Therefore, the equation of the line that passes through the points A (0, 0), B (2, 3), C (4, 6), and D (8, 12) is y = (3/2)x.