Question

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.

Answer 1

Answer: Line A slope = 4 and Line B slope =

Δy

Δx

=

7

2

= 3.5. Line A has a greater slope than line B.

Answer 2

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

Explanation:

The equation of the line A is
`y=4x-9`

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

`y=mx+b`

The slope
`m` of the line B is

`m=(12-5)/(2-0)=(7)/(2) =3.5`

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

`y=3.5+b\\\\5=3.5(0)+b\\\\b=5`

Thus we have the equation of the line
`b`

`y=3.5x+5`

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.