The two functions 2 .The slope of Function A is less than the slope of Function B. Therefore , 2 .The slope of Function A is less than the slope of Function B is correct .
The slope of a linear function is indeed represented by the coefficient of the x term in its equation.
In the case of Function A, where the coefficient of the x term is 3, and Function B, where it is 10, it is correct to assert that the slope of Function B is greater than that of Function A.
This is because the coefficient reflects the rate of change of the dependent variable (y) with respect to the independent variable (x).
Now, addressing the other options:
The two functions have different y-intercepts, but their slopes are equal:
This statement contradicts the information given. If the slopes are different, the functions cannot have equal slopes.
The y-intercept of Function A is greater than the y-intercept of Function B:
There is no information provided about the y-intercepts of the two functions in the given context.
It is simple to calculate Function A's slope between the positions where the x-values differ by one:
The formula is m = (y3 -y2)/(x3 -x2) = (24-22)/(10-9) = 2/1 = 2.
Fun A has a 2 slope.
The coefficient of x in equation (3) represents the slope of function B.
Function A's y-intercept can be obtained by using point-slope form first: y -22 = 2(x -9) y equals 2x -18 + 22.
Slope-intercept form for y = 2x + 4
The intercept of Function B and +4 are same.
Question
Function A and Function B are linear functions. Compare the two functions and choose all that are correct.
1. The slope of Function A is greater than the slope of Function B.
2 .The slope of Function A is less than the slope of Function B.
3. The y-intercept of Function A is greater than the y-intercept of Function B.
4 .The y-intercept of Function A is less than the y-intercept of Function B.