Question

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 1

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

Step-by-step explanation

the point-slope formula says

`\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}`

so

Step 1

find the slope of the line:

to find the slope we need to use the formula

`\begin{gathered} slope=(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}`

so

a)let

`\begin{gathered} P1(2,-3)\text{ } \\ P2(-2,3) \end{gathered}`

b) now replace in the formula

`\begin{gathered} slope=(y_(2)-y_(1))/(x_(2)-x_(1)) \\ slope=(3-(-3))/(-2-2)=(6)/(-4)=-(3)/(2) \end{gathered}`

so, the slope is -3/2

Step 2

now, we can replace in the point-slope formula

a)let

`\begin{gathered} P1(2,-3) \\ slope=m=-(3)/(2) \end{gathered}`

b) now, replace

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

so, the answer is

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

I hope this helps you