Consider two lines. line a is given by the function f(x) = 4x − 9, while line b contains the points (0, 5) and (2, 12). which statement is true? a) line a and line b have the same slope. b) line a has a greater slope than line b. c) line b has a greater slope than line a. d) line a slope is less than the slope of line b.

B) Line A has a greater slope than Line B.

Step-by-step explanation:

The equation of the line A is

The equation of the line B can be written in the y-intercept form as

The slope of the line B is

and the y-intercept of the line can be found from the point (0,5) as follows:

Thus we have the equation of the line

Now we are ready to compare the lines A and B, and let us start by considering each of the choices.

(A). Line A and line B have the same slope.

The slope of line A is 4, and of line B is 3.5—they are not the same.

(B). The line A has a greater slope than line B.

The slope of line A is 4, and of line B is 3.5—yes the slope of line A is greater than line B.

(C). Line B has a greater slope than line B.

No this is not true, because we already saw  that slope of line A is greater than of line B.

(D). Line A slope is less than the slope of line B.

Not true either. Because the slope of line A is greater than B.

Thus only choice A is correct.