Question

Choose the point slope form of the equation below that represents the line that passes through the points -3, 2 and 2, 1

Answer 1

Hello!!

So, the point slope equation is y-y₁=m(x-x₁)

In order to solve this with the points (-3,2) and (2,1), you need to find the slope.

The equation to find the slope is m=(y₂-y₁)/(x₂-x₁):

m=(2-1)/(-3-2)

m= -1/5

So your slope is-1/5

Now, using the point slope equation I stated earlier, ^^^ plug in either of the points you were given (Either -3,2 or 2,1) and your slope or m value (-1/5)

I'll show you both of the possible equations:

1) Using (-3,2)

y-(2)=m(x-(-3)) OR y-(2)=m(x+3)

Add 2 to both sides

y=mx+5

Answer is y=mx+5

2) Using (2,1)

y-(1)=m(x-(2))

Add 1 to both sides

y=mx-1

Answer is y=mx-1


Hope this helps!!!!

Answer 2

`y=-(x)/(5)+(7)/(5)`

Explanation:

We need to find the equation of a line that passes through the points
`\left ( -3, 2 \right )` and
`\left ( 2, 1 \right )`.

We know that the point slope form of a line passing through
`\left ( x_(1), y_(1) \right )` and with slope m is
`y-y_(1)=m\left ( x_(1)-y_(1) \right )`

So, first we need to find the slope, m.

We know that
`m=(y_(2)-y_(1))/(x_(2)-x_(1))}`

Here,
`x_(1)=-3, x_(2)=2, y_(1)=2,y_(2)=1`

So,
`m=(1-2)/(2-(-3))=-(1)/(5)`

Now, the equation of the line is

`y-2=-(1)/(5)\left ( x-\left ( -3 \right ) \right )`

`\implies y-2=-(1)/(5)\left ( x+3 \right )`

`\implies y-2=-(x)/(5)-(3)/(5)`

`\implies y=-(x)/(5)-(3)/(5)+2`

`\implies y=-(x)/(5)+(7)/(5)`

Hence, the equation is
`y=-(x)/(5)+(7)/(5)`