Question

Which function is increasing at the highest rate? A. B. A linear function on a coordinate plane passes through (minus 1, 3), and (2, minus 3) which intercepts axis at (0.5, 0), and (0, 1) C. A linear function, f, with an x-intercept of 8 and a y-intercept of -4. D. x 1 2 3 4 5 g(x) -5 -4 -3 -2 -1

Answer 1

The highest rate on increasing is of 12x -6y = -24; Option B is the correct answer.

The options are given in the image attached with the answer

What is a Function ?

A function is a law that relates a dependent variable and an independent variable.

It is asked among the options given , which is increasing at the highest rate.

To increase at a rate , the value of the slope , m should be > 0

For the Option 1

for a straight line function , the slope is given by

m = ( y₂ -y₁)/(x₂-x₁)

m = ( -3 -3)/(2- (-1)) = -6 /3 = -2

Therefore the function is decreasing

For Option 2

12x - 6y = -24

-6y = -12x -24

y = 2x +4

m = 2 (increasing)

For option 3

m = (-4 + 5)/(2-1) = 1

For Option 4

(8,0) (0,-4)

m = (-4 -0) /(0-8) = 4/8 = 1/2

The highest rate on increasing is of 12x -6y = -24

Therefore Option B is the correct answer.

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