Question

Which function is increasing at the highest rate?

OA
B. 12. - 6y =
C. x 1
–24
2
3
g(x)
5
I
4
D.
A linear function, f, with an x-intercept of 8 and a y-intercept of -4.

Answer 1

B

Explanation:

Answer 2

Option B:
`12x - 6y = -24`

Explanation:

A function is said to be increasing if it has a slope greater than 0.

The function with the largest slope has the highest increasing rate.

Here, for the graph in option A, the function is decreasing with increasing
`x`. So, it has a negative slope.

We need to convert equation of option B into standard form and then determine its slope.

The standard form of a straight line is
`y = mx + b`, where
`m` is the slope of the line and
`b` is the y-intercept.

Now, given function is:

`12x - 6y = -24\\ 6y = 12x + 24\\ y = (12)/(6)x+(24)/(6)\\ y = 2x + 4`

Therefore, the slope is 2.

Option C:

Slope is given as,

`m_(C)=(g(x_(2)-g(x_(1)))/(x_(2)-x_(1)) =(-4-(-5))/(2-1)=(-4+5)/(1)=1`

Therefore, the slope is 1.

Option D:

Equation of a line with
`a` and
`b` as
`x` and
`y` intercepts is given as,

`(x)/(a)+(y)/(b)=1`

Here,
`a = 8` and
`b = -4`

∴
`(x)/(8)+(y)/(-4)=1\\ (x-2y)/(8)=1\\ x-2y=8\\ 2y=x-8\\y=(1)/(2)x-4`

Therefore, the slope is
`(1)/(2)`.

Hence, the largest slope is for option B and thereby the highest increasing rate.