Final answer:
The correct equation for the standard form of the line with an X-intercept of -4 and a Y-intercept of 3 is -4x + 3y = 12. We find this by setting x to -4 and y to 0 for the X-intercept, and x to 0 and y to 3 for the Y-intercept, and solving for the constants A, B, and C in standard form.
Step-by-step explanation:
To complete the equation for the standard form of the line that has an X-intercept of -4 and a Y-intercept of 3, we need to use the intercepts to define the line. The standard form of a line equation is Ax + By = C, where A, B, and C are integers. The X-intercept is the point where the line crosses the x-axis (where y = 0), and the Y-intercept is the point where the line crosses the y-axis (where x = 0).
Using the X-intercept of -4, we plug x = -4 into the standard form when y = 0, which would give us -4A = C. Using the Y-intercept of 3, we plug y = 3 into the standard form when x = 0, which gives us 3B = C. As a result, the two equations we get are:
Since both expressions equal C, they are also equal to each other: -4A = 3B. To find a suitable A and B that satisfy both intercepts and are integers, we can take A = -3 and B = 4. Then the value of C would be -4(-3) = 3(4) = 12. Thus, the standard form of the line equation with the given intercepts is -4x + 3y = 12, which is option B).