Question

Find the slope of #1 y = 2x - 3#2 (-2,-4) (-1,-2)#3 y = 1/3x - 4# 4 (4,0) (4,1)

Answer 1

1. slope= 2

2. slope=2

3. slope= 1/3

4. slope indefinite, vertical line

Step-by-step explanation

Step 1

`\begin{gathered} y=\text{ 2x-3} \\ \end{gathered}`

the equation is given in slope(m) - intercept(b)

`\begin{gathered} y=\text{ mx+b} \\ \text{then} \\ mx+b=2x-3 \\ m=2 \\ \text{slope}=2 \end{gathered}`

Step 2

when you have two points of a line, P1 and P2 the slope is given by:

`\begin{gathered} \text{slope}=(y_2-y_1)/(x_2-x_1) \\ \text{where} \\ P1(x_1,y_1)andP2(x_2,y_2) \end{gathered}`

Let

P1(-2,-4) P2(-1,-2)

replace

`\begin{gathered} \text{slope}=(y_2-y_1)/(x_2-x_1) \\ \text{slope}=(-2-(-4))/(-1-(-2)) \\ \text{slope}=(-2+4)/(-1+2)=(2)/(1)=2 \\ \text{slope}=2 \end{gathered}`

Step 3

`y=(1)/(3)x-4`

similar to the #1. ,the equation is given in slope(m) - intercept(b)

`\text{the slope = }(1)/(3)`

Step 4

let

`P1(4,0)\text{ and P2(4,1)}`