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

Slope of a line is the measure of its steepness. The description that compares two functions is: Option B: The line for function A is steeper.

How to get the slope intercept form of a straight line equation?

If the slope of a line is m and the y-intercept is c, then the equation of that straight line is given as:

$y = mx +c$

What is the equation of a line passing through two given points in 2 dimensional plane?

Suppose the given points are $(x_1, y_1)$ and $(x_2, y_2)$ , then the equation of the straight line joining both two points is given by

$(y - y_1) = \dfrac{y_2 - y_1}{x_2 - x_1} (x -x_1)$

For the second function, we have two pairs of points as

$(x_1, y_1) = (0,-2)\\(x_2, y_2) = (3,-1)$

Thus, the equation of the line representing the function B is

$(y - y_1) = \dfrac{y_2 - y_1}{x_2 - x_1} (x -x_1)\\\\y - (-2) = \dfrac{-1 - (-2)}{3-0}(x - 0)\\\\y + 2 = \dfrac{1}{3}x\\\\y = 0.3\overline{3}x - 2$

Since slope of line representing first function is bigger than slope of line representing second function and the bigger the slope is, the steeper it is. So line representing function A is steeper than line representing function B.

And we see that both lines have same y intercept, so the intercepts coincide on the y-axis.

Thus,

The description that compares two functions is given as

Option B: The line for function A is steeper.

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