Which function has the greatest rate of change? a. x y 3 3 4 6 5 9 b. y = 4 + 6x c. 12x + 6y = 18 d. a linear function that goes through point 1, negative 1 and point 0, 4

B. y = 4 +  6x

Step-by-step explanation:

We know that the rate of change of a straight line is equal to the slope of the line.

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

Also, the slope of a line joined by and is given by .

So, using these, we will find the slopes of the lines given in the options.

A. Here, we are given two points (3,3) and (4,6). Then, the slope is given by,

i.e. .

B. We have the equation of line y = 4 + 6x. On comparing it with the general form, we get that the slope is 6 i.e. .

C. We are given the standard form of a line. First, we convert it into the slope-intercept form ( or the general form ).

i.e. 12x + 6y = 18 → 2x + y = 3 → y = -2x + 3

Now, on comparing this equation with the general form of a line, we get that the slope is -2. i.e. .

D. Here, we are given a linear function passing through (1,-1) and (0,4). Then the slope is given by,

i.e. .

Hence, we obtain that the function y=4+6x has the greatest slope or the greatest rate of change i.e. .

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step-by-step explanation: