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.

Question

asked Oct 23, 2020 68.8k views

2 Answers

Xvatar · Answer 1 · 2020-10-27T09:29:37+0000

Answer:

Option B:

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
. 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
is the slope of the line and
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
and
as
and
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
.

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