Final answer:
To calculate the y-intercept using two points, find the slope and use point-slope form of the line equation. Using the point (2, 300) and the calculated slope, we found the y-intercept to be 142.86.
Step-by-step explanation:
To calculate the y-intercept, we first need to find the slope of the line passing through the two given points (2, 300) and (16, 1400). The slope (m) can be found by taking the difference in y-coordinates and dividing it by the difference in x-coordinates:
m = (1400 - 300) / (16 - 2) = 1100 / 14 ≈ 78.57.
Now that we have the slope, we can use the point-slope form of the line equation, which is y - y1 = m(x - x1), where (x1, y1) is one of our points. Let’s use (2, 300):
y - 300 = 78.57(x - 2).
To find the y-intercept, we solve for y when x = 0:
y - 300 = 78.57(0 - 2)
y - 300 = -157.14
y = 300 - 157.14 = 142.86.
Therefore, the y-intercept of the line is 142.86.