We need to find the slope-intercept equation for all cases:
Function 1.
In this case, we have the following points
[tex]\begin{gathered} (x_1,y_1)=(1,-2) \\ (x_2,y_2)=(0,-4) \end{gathered}[/tex]
Then, its slope is given by
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{-4+2}{0-1}=2[/tex]
Since the line crosses the y-axis at y=-4, the line equation is:
[tex]y=2x-4[/tex]
Function 2.
We can choose 2 points of the table, for instance,
[tex]\begin{gathered} (x_1,y_1)=(0,5) \\ (x_2,y_2)=(1,4) \end{gathered}[/tex]
and get the following slope
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{4-5}{1-0}=-1[/tex]
since the line crosses at y=5, the equation is:
[tex]y=-x+5[/tex]
Function 3.
From the given information, the equation is
[tex]y=-4x-1[/tex]
Function 4.
From the given information, the equation is:
[tex]y=5x+2[/tex]
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
