Question

Which description best compares the graphs of the two functions below?

Answer 1

Answer:

The description that best compares the graph of the two function is:

          The line for function A is steeper.

Step-by-step explanation:

Function: A is given by:

          $y=3x-2$

and   Function: B is given by the help of a equation:

      $y=\dfrac{1}{3}x-2$

( since from the table we may see that with a increase of x by 3 units the y-value also increases by 1 units.

This means that the slope is constant and hence the function is linear.

As we see that the function passes through (0,-2) and (6,0)

Hence, the equation is given by:

$y-(-2)=\dfrac{0-(-2)}{6-0}\times (x-0)\\\\\\y+2=\dfrac{2}{6}x\\\\\\y+2=\dfrac{1}{3}x\\\\\\y=\dfrac{1}{3}x-2$  

)

• We know that a y-intercept is a point where x=0

                   y-intercept of Function A is: -2

            and y-intercept of Function B is: -2

    Hence, both functions have the same y-intercept.

• The greater the slope the steeper the line.

             Slope of function A is: 3

          and slope of function B is: 1/3

     As the slope of function A is more than function B.

           Hence, the line for function A is steeper.

Answer 2

Some of your pic is cut off so it's difficult to give the exact answer.  But if you plot the points from the table you get that the equation for that set of data is linear and is y = 1/3x -2.  This tells me that the y-intercepts are the same for both equations, so your answer is not the first or the third.  Because the slope of the function A is 3 and for B is 1/3, the line for function A is steeper, the second of your choices above.