Which statement correctly compares the function shown on this graph with
the function y= 4x+2?
1 2 3 4 5
O A The function shown on the graph has a greater rate of change and
a higher starting point
O B. The function shown on the graph has a smaller rate of change, but
a higher starting point
O C. The function shown on the graph has a smaller rate of change and
a lower starting point
O D. The function shown on the graph has a greater rate of change but
a lower starting point

PLEASE ANSWER

Answer:

B. The function shown on the graph has a smaller rate of change, but a higher starting point.

Step-by-step explanation:

Rate of change = slope of a linear graph.

Given the linear function, [tex] y = 4x + 2 [/tex] , the rate of change here is represented by the slope of the line, which is 4.

Let's find the rate change of the function represented on the graph using slope formula:

Rate of change = [tex] \frac{y_2 - y_1}{x_2 - x_1} [/tex]

Use coordinates of any two points on the line. Let's take,

[tex] (0, 4) = (x_1, y_1) [/tex]

[tex] (1, 7) = (x_2, y_2) [/tex]

Rate of change = [tex] \frac{7 - 4}{1 - 0} = \frac{3}{1} = 3 [/tex]

Rate of change of the linear function of the graph = 3.

Thus the function on the graph has a smaller rate of change, than the function, y = 4x + 2.

The starting value of a function is the y-intercept, that is, the value of y, when x = 0. It is the point at which the line intercepts the y-axis.

The starting value of the linear function, y = 4x + 2 is 2.

The starting value of the function on the graph is 4. At this point, x = 0.

Thus, the function on the graph has a higher starting point.

The statement that correctly compares the function shown on this graph with the function y= 4x+2 is:

B. The function shown on the graph has a smaller rate of change, but a higher starting point.

Answer:

A

Step-by-step explanation:

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