Question

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

Answer 1

Answer:

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 $( x_{1},y_{1} )$ and $( x_{2},y_{2} )$ is given by $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$.

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,

$m_{1}=\frac{6-3}{4-3}$ i.e. $m_{1}=3$.

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. $m_{2}=6$.

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. $m_{3}=-2$.

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

$m_{1}=\frac{4+1}{0-1}$ i.e. $m_{4}=-5$.

Hence, we obtain that the function y=4+6x has the greatest slope or the greatest rate of change i.e. $m_{2}=6$.