Final answer:
To find the value of y when x = 20 for a line with a y-intercept of 12 and an x-intercept of 4, calculate the slope as -3, and derive the equation y = -3x + 12. Substituting x = 20, y equals -48, which does not match any of the provided options.
Step-by-step explanation:
To find the value of y when x = 20 for a line with a y-intercept of 12 and an x-intercept of 4, we first need to determine the slope of the line (m).
The slope can be found using the formula m = (change in y) / (change in x).
In this case:
- The change in y is from 12 (at the y-intercept) to 0 (at the x-intercept).
- The change in x is from 0 (at the y-intercept) to 4 (at the x-intercept).
Thus, m = (0 - 12) / (4 - 0) = -3.
The equation of the line is then y = mx + b, where b is the y-intercept. Substituting the known values: y = -3x + 12.
To find y when x = 20:
y = -3(20) + 12
y = -60 + 12
y = -48
Therefore, the value of y when x = 20 is -48, which is not one of the provided options and suggests there may be an error in the options given.