Compare the following functions.
Equation A: 6x+2y=14
Equation B: 12x−4y=−8
Which statement about the functions is true?
A. The slopes and the y-intercepts of both functions are different
B. The y-intercepts of both functions are the same
C. The slopes and the y-intercepts of both functions are the same
D. The slopes of both functions are the same
To compare the functions, let's put them in slope-intercept form (y = mx + b) where m is the slope and b is the y-intercept.
For Equation A:
6x + 2y = 14
Subtract 6x from both sides:
2y = -6x + 14
Divide everything by 2:
y = -3x + 7
For Equation B:
12x - 4y = -8
Subtract 12x from both sides:
-4y = -12x - 8
Divide everything by -4:
y = 3x + 2
Comparing the equations, we can see that the slopes of both functions are different. In Equation A, the slope is -3, and in Equation B, the slope is 3. Therefore, the correct statement is:
A. The slopes and the y-intercepts of both functions are different