Question

I need to know what are the answers for 5,6,7.

Answer 1

Question 5:

The first question gives us the following points:

`\lbrace(-1,-2),(3,0)\rbrace`

To calculate the slope, we use the following formula:

`m=(y_2-y_1)/(x_2-x_1)`

using our set of points, we get the following slope:

`(0-(-2))/(3-(-1))=(2)/(4)=(1)/(2)=0.5`

The line equation, have the following format:

`y=mx+B`

Since we have two points and the slope, we can substitute them in this equation and get the 'b' coefficient.

(We're going to use P1 because the question asks for it, but using P2 it would also work)

`y=mx+B\Leftrightarrow-2=(1)/(2)*(-1)+B`

Solving for 'B':

`-2=-0.5+B\Rightarrow B=-(3)/(2)=-1.5`

With this, we have the following equation for those points:

`y=0.5x-1.5`

Question 6:

Solving in an analogous way

Our set of points:

`\lbrace(-14,-17),(-4,-12)\rbrace`

The slope m:

`((-12)-(-17))/((-4)-(-14))=(5)/(10)=(1)/(2)=0.5`

Plugging the slope and P1 into the line equation:

`y=mx+B\Leftrightarrow-17=(1)/(2)*(-14)+B`

Solving for 'B':

`-17=-7+B\Rightarrow B=-10`

Line Equation:

`y=0.5x-10`

Question 7:

Solving in an analogous way

Our set of points:

`\lbrace(0,0),(14,15)\rbrace`

The slope m:

`(15-0)/(14-0)=(15)/(14)=1.07142857143`

Plugging the slope and P1 into the line equation:

`y=mx+B\Leftrightarrow0=(14)/(15)*0+B`

Solving for 'B':

`0=0+B\Rightarrow B=0`

Line Equation:

`y=(14)/(15)x`