Final answer:
The equation of the line with an x-intercept at 4 and a y-intercept at 6 is y = -3/2x + 6, which corresponds to option B.
Step-by-step explanation:
To find the equation of a line that has an x-intercept at 4 and a y-intercept at 6 in slope-intercept form, you start with the general formula for a line, which is y = mx + b, where m is the slope, and b is the y-intercept. In this case, we know the y-intercept (b) is 6. To find the slope (m), we consider the x-intercept at (4,0) and the y-intercept at (0,6). The slope is the change in y divided by the change in x, or (rise/run). Therefore, from (4,0) to (0,6), the rise is 6 and the run is -4, which gives us a slope of m = -6/4 = -3/2.
The equation of the line is thus y = -3/2x + 6. Among the choice given, the correct one is B. y = -3/2x + 6.