Which of the following point-slope form equations could be produced with the points (2, -3) and (-2, 3)?O y + 3 = 3/2(x - 1)O y + 3 = -3/2(x - 2)Oy + 2 = -3/2(x - 2)Oy + 2 = 3/2(x - 1)

Answer :

y + 3 = -3/2(x - 2)

Explanation

the point-slope formula says

[tex]\begin{gathered} y-y_1=m(x-x_1) \\ where \\ m\text{ is the slope} \\ P1(x_1,y_1)\text{ is a well know point from the line} \end{gathered}[/tex]

so

Step 1

find the slope of the line:

to find the slope we need to use the formula

[tex]\begin{gathered} slope=\frac{y_2-y_1}{x_2-x_1} \\ where \\ P1(x_1,y_1) \\ and \\ P2(x_2,y_2) \\ are\text{ 2 points from the line} \end{gathered}[/tex]

so

a)let

[tex]\begin{gathered} P1(2,-3)\text{ } \\ P2(-2,3) \end{gathered}[/tex]

b) now replace in the formula

[tex]\begin{gathered} slope=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ slope=\frac{3-(-3)}{-2-2}=\frac{6}{-4}=-\frac{3}{2} \end{gathered}[/tex]

so, the slope is -3/2

Step 2

now, we can replace in the point-slope formula

a)let

[tex]\begin{gathered} P1(2,-3) \\ slope=m=-\frac{3}{2} \end{gathered}[/tex]

b) now, replace

[tex]\begin{gathered} y-y_{1}=m(x-x_{1}) \\ y-(-3)=-\frac{3}{2}(x-2) \\ y+3=-\frac{3}{2}(x-2) \end{gathered}[/tex]

so, the answer is

y + 3 = -3/2(x - 2)

I hope this helps you