Question

Which equation describes the line whose x-intercept is (4,0) and whose y-intercept is (0, -3)?

A. y=4x−3
B. y=4x−3
C. y=−4x+4
D. y=−3x+4

Answer 1

The line with x-intercept (4,0) and y-intercept (0, -3) has a slope of 3/4. Using the slope-intercept form, the equation of the line is y = (3/4)x - 3, but this option is not available in the given choices suggesting a mistake in the question's answer options.

Step-by-step explanation:

To find the equation of the line with given x-intercept (4,0) and y-intercept (0, -3), we first need to determine the slope of the line. The slope (m) of a line is the rise over the run, which in this case is the change in y divided by the change in x. Using the coordinates of the intercepts, the slope can be calculated as follows:

m = (y2 - y1) / (x2 - x1) = (-3 - 0) / (0 - 4) = 3/4

Now, using the slope-intercept form of a line, y = mx + b, where m is the slope and b is the y-intercept, we substitute the known values m = 3/4 and b = -3 to get:

y = (3/4)x - 3

This equation is not listed among the options, indicating a potential mistake in the question. Options A and B are duplicates and C and D have different slopes and y-intercepts that do not match the given intercepts. Therefore, we can assume the intercepts given do not generate the options provided in the answer choices.