Question

Plot three points for the line and graph the line. Point (-4, 2) slope -4/3

Answer 1

`\begin{gathered} P(0,(22)/(3)) \\ P(1,(26)/(3)) \\ P(-1,6) \end{gathered}`

Step-by-step explanation

when you have the slope and a point of the line, you can find the equation by using Point-slope is the general form

`y-y_(1)=m\mleft(x-x_(1)\mright)`

where

`\begin{gathered} \text{m is the slope and} \\ (x_1,y_1)\text{ is a point of the line} \end{gathered}`

so

Step 1

Let

slope=-4/3

point=(-4,2)

replace and isolate y

`\begin{gathered} y-y_1=m\mleft(x-x_1\mright) \\ y-2=(4)/(3)(x-(-4)) \\ y-2=(4)/(3)x+(16)/(3) \\ ad\text{d 2 in both sides} \\ y-2+2=(4)/(3)x+(16)/(3)+2 \\ y=(4)/(3)x+(22)/(3) \end{gathered}`

so, the equation of the line is

`y=(4)/(3)x+(22)/(3)`

Step 2

plot 3 points

to do that, replace in the equation and you will get the y -coordinate

so

a) when x=0

`\begin{gathered} y=(4)/(3)\cdot0+(22)/(3) \\ y=0+(22)/(3) \\ y=(22)/(3) \\ P(0,(22)/(3)) \end{gathered}`

b) when x= 1

`\begin{gathered} y=(4)/(3)\cdot1+(22)/(3) \\ y=(4)/(3)+(22)/(3) \\ y=(26)/(3) \\ P(1,(26)/(3)) \end{gathered}`

c) when x= -1

`\begin{gathered} y=(4)/(3)\cdot-1+(22)/(3) \\ y=-(4)/(3)+(22)/(3) \\ y=(18)/(3)=6 \\ P(-1,6) \end{gathered}`

Step 3

finally, draw a line that passes through the points

I hope this helps you