Question

Which statement correctly compares the function shown on this graph with the function y = 6x - 1?

Answer 1

Answer:

we conclude that the function shown in the graph has a smaller rate of change and a lower starting point.

Therefore, option (A) is true.

Step-by-step explanation:

FUNCTION

Given the function

y = 6x - 1

Comparing with the slope-intercept form of the graph

y = mx+b

where m is the slope and b is the y-intercept

Thus,

The slope of the function  = rate of change = 6

The starting point of the function can be obtained by setting x = 0 and solve for y

i.e

at x = 0, y = 6x-1 = 6(1)-1 = 5

Thus,

The starting point of the function is (0, 5)

                 

LINE GRAPH

Now, consider the line graph

Taking two points to find the slope

• (0, -6)

• (2, 4)

$\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}$

$\left(x_1,\:y_1\right)=\left(0,\:-6\right),\:\left(x_2,\:y_2\right)=\left(2,\:4\right)$

$m=\frac{4-\left(-6\right)}{2-0}$

$m=5$

Thus,

The slope of the line graph  =  rate of change = 5

From the graph, it is clear that at x=0, the value of y=6

Thus,

The starting point of the graph is (0, -6)

Thus,

FOR FUNCTION

The slope of the function  = rate of change = 6

The starting point of the function is (0, 5)

FOR LINE GRAPH

The slope of the line graph  = rate of change = 5

The starting point of the graph is (0, -6)

Conclusion

Hence, we conclude that the function shown in the graph has a smaller rate of change and a lower starting point.

Therefore, option (A) is true.