Question

I have to figure out the slope and y-intercept and answer the questions

Answer 1

Function 1

Let us calculate the equation of the line of function 1 picking any two points

The two points picked are (1 , 0) and (0 , -4)

The formula for the equation given two points is

`(y-y_1)/(x-x_1)=(y_2-y_1)/(x_2-x_1)`

Given:

`x_1=1,y_1=0,x_2=0,y_2=-4`

Hence,

`\begin{gathered} (y-0)/(x-1)=(-4-0)/(0-1) \\ (y)/(x-1)=(-4)/(-1) \\ (y)/(x-1)=4 \\ \text{Cross}-\text{ multiply} \\ y=4(x-1) \\ y=4x-4 \end{gathered}`

Therefore, the equation for the function is

`y=4x-4`

Where, the coefficient of x is the slope and the constant variable is the y-intercept.

Hence,

`\text{slope(m)}=4,\text{ y-intercept = -4}`

Function 2

Let us calculate the equation of the line of function 2 picking any two points from the data in the table.

The two points picked are (-2 , 8) and (2 , -12)

Therefore,

`x_1=-2,y_1=8,x_2=2,y_2=-12`

Hence,

`\begin{gathered} (y-8)/(x-(-2))=(-12-8)/(2-(-2)) \\ (y-8)/(x+2)=(-20)/(2+2) \\ (y-8)/(x+2)=-(20)/(4) \\ (y-8)/(x+2)=-5 \\ \text{Cross}-mu\text{ltiply} \\ y-8=-5(x+2) \\ y-8=-5x-10 \\ y=-5x-10+8 \\ y=-5x-2 \end{gathered}`

Where,

`\begin{gathered} \text{Slope(m)}=-5, \\ y-\text{intercept = -2} \end{gathered}`

Function 3

The given equation is

`\begin{gathered} y=2x+1 \\ \text{where,} \\ \text{slope = 2} \\ y-\text{intercept}=1 \end{gathered}`

Function 4

Given:

`\begin{gathered} \text{slope = -1} \\ y-\text{intercept}=3 \end{gathered}`

Hence,

a) The functions that have graphs with slopes less than 3 are Function 2, Function 3 and Function 4.

b) The function that has the graph with a y-intercept closest 0 is Function 3.

c) The function that has the graph with greatest y-intercept is Function 4.