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

Answer:

$y=-\frac{x}{5}+\frac{7}{5}$

Step-by-step 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 $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}}$

Here, $x_{1}=-3, x_{2}=2, y_{1}=2,y_{2}=1$

So,  $m=\frac{1-2}{2-(-3)}=-\frac{1}{5}$

Now, the equation of the line is

$y-2=-\frac{1}{5}\left ( x-\left ( -3 \right ) \right )$

$\implies y-2=-\frac{1}{5}\left ( x+3 \right )$

$\implies y-2=-\frac{x}{5}-\frac{3}{5}$

$\implies y=-\frac{x}{5}-\frac{3}{5}+2$

$\implies y=-\frac{x}{5}+\frac{7}{5}$

Hence, the equation is $y=-\frac{x}{5}+\frac{7}{5}$