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Daniel [21]
4 years ago
11

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

Mathematics
2 answers:
padilas [110]4 years ago
8 0

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}

lions [1.4K]4 years ago
5 0
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!!!!
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