The description below represents Function A and the table represents Function B:
Function A
The function is 2 more than 5 times x.
Function B
x y
-1 2
0 5
1 8
Which statement is correct about the slope and intercept of the two functions?
Their slopes are equal but y-intercepts are not equal.
Their slopes are not equal but y-intercepts are equal.
Both slopes and y-intercepts are equal.
Neither slopes nor y-intercepts are equal.
To determine the slope and y-intercept of the two functions, we need to analyze their equations.
Function A is described as "2 more than 5 times x," which can be written as:
A: y = 5x + 2
Function B is represented by the table of values:
B:
x y
-1 2
0 5
1 8
To determine the slope of Function A, we can observe that the coefficient of x is 5. Therefore, the slope of Function A is 5.
To determine the y-intercept of Function A, we can observe that the constant term is 2. Therefore, the y-intercept of Function A is 2.
To determine the slope of Function B, we can use the formula:
slope = (change in y)/(change in x)
By examining the given table of values for Function B, we can see that the change in y for each change in x is constant:
For x = -1 to x = 0:
change in y = 5 - 2 = 3
For x = 0 to x = 1:
change in y = 8 - 5 = 3
Therefore, the slope of Function B is 3.
To determine the y-intercept of Function B, we can observe the y-value when x is 0. From the table, we can see that when x = 0, y = 5.
Therefore, the y-intercept of Function B is 5.
Comparing the slopes and y-intercepts of the two functions:
The slope of Function A is 5, while the slope of Function B is 3. Therefore, the slopes are not equal.
The y-intercept of Function A is 2, and the y-intercept of Function B is 5. Therefore, the y-intercepts are also not equal.
So the correct statement is:
Their slopes are not equal but y-intercepts are not equal.
To determine the slope and y-intercept of the two functions, we need to analyze the given information.
Function A is described as "2 more than 5 times x." This can be expressed mathematically as:
A: y = 5x + 2
The slope of Function A is the coefficient of x, which is 5. The y-intercept is the constant term, which is 2.
Function B is represented in a table with x and y values. From the table, we can deduce that:
B: y = 3x + 5
Taking the first row of the table (-1, 2), we can substitute the values into the equation above and solve for the slope:
2 = 3(-1) + 5
2 = -3 + 5
2 = 2
Since the equation is true, we can determine that the slope of Function B is also 3.
By comparing the slopes and y-intercepts of the two functions, we can conclude that their slopes are not equal (Function A has a slope of 5 while Function B has a slope of 3), but their y-intercepts are equal (both functions have a y-intercept of 2).
Therefore, the correct statement is: "Their slopes are not equal but y-intercepts are equal."
Function A: F(x) - 5x + 2.
Function B: F(x) = mx + b.
P1(-1,2), P2(1,8).
m = (y2-y1)/(x2-x1) = (8-2)/(1-(-1) = 6/2 = 3.
Y = mx + b.
2 = 3*(-1) + b
b = 5.
Function B: F(x) = 3x + 5.