Question

What is the equation of the graphed line in point-slope form? y – 1 = 2/3 (x + 3), y – 1 = 2/3 (x – 3), y + 1 = 2/3 (x – 3), y + 1 = 2/3 (x + 3) (Points are at (-3,-3) and (3,1)

Answer 1

Hello!

First of all we need to find the slope. To do so we use the following equation.

$\frac{ y_{2}- y_{1} }{ x_{2}- x_{1} }$

The ones and twos just represent different ordered pairs. We will have (-3,3) be ($x_{1} , y_{1}$) and (3,1) be ($x_{2} , y_{2}$) Now we plug our numbers into the formula.

$\frac{1+3}{3+3} = \frac{4}{6} = \frac{2}{3}$
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Now we need to write our equation in point-slope form, which is y-k=m(x-h), where (h,k) represent a point on the line, and m is the slope.. We will use (3,1) for (h,k). Our final equation is shown below.

y-1= $\frac{2}{3}$(x+3)

I hope this helps!