Question

(a) Which function has the graph with a y-intercept closest to 0 ?(b) Which function has the graph with the greatest slope?(c) Which functions have graphs with y-intercepts greater than 3? (Check all that apply.)

Answer 1

We need to find the slope-intercept equation for all cases:

Function 1.

In this case, we have the following points

`\begin{gathered} (x_1,y_1)=(1,-2) \\ (x_2,y_2)=(0,-4) \end{gathered}`

Then, its slope is given by

`m=(y_2-y_1)/(x_2-x_1)=(-4+2)/(0-1)=2`

Since the line crosses the y-axis at y=-4, the line equation is:

`y=2x-4`

Function 2.

We can choose 2 points of the table, for instance,

`\begin{gathered} (x_1,y_1)=(0,5) \\ (x_2,y_2)=(1,4) \end{gathered}`

and get the following slope

`m=(y_2-y_1)/(x_2-x_1)=(4-5)/(1-0)=-1`

since the line crosses at y=5, the equation is:

`y=-x+5`

Function 3.

From the given information, the equation is

`y=-4x-1`

Function 4.

From the given information, the equation is:

`y=5x+2`

In summary, we have obtained the following equations:

1) y=2x-4

2) y=-x+5

3) y=-4x-1

4) y=5x+2

Then, we have obtained:

a) Which function has the graph with a y-intercept closest to 0? Answer. As we can note, function 3 because its y-intercept is -1

(b) Which function has the graph with the greatest slope? Answer. From the above result, we can note that function 4 has the greatest slope because it is equal to 5

(c) Which functions have graphs with y-intercepts greater than 3? Answer. Only function 2 has y-intercept greater than 3 because the value is 5

In summary, the answers are:

a) Function 3

b) Function 4

c) Function 2