Question

Which of the following are point-slope equations of the line going through(-2,-2) and (2, 1)? Check all that apply.A. y-1 =3/4(x-2)B. y-2=-3/4(x-1)C. y-1=-3/4 (x-2)D. y+2 = 3/4(x+2)E. y-2 = 3/4(x-2)F. y+2 =-3/4(x+2)

Answer 1

The given points are (-2, -2) and (2, 1).

First, we have to find the slope.

$m=\frac{y_2-y_1}{x_2-x_1}$

Let's replace the points in the formula.

$m=\frac{1-(-2)}{2-(-2)}=\frac{1+2}{2+2}=\frac{3}{4}$

Now, we use one point, the slope, and the point-slope formula.

$\begin{gathered} y-y_1=m(x-x_1) \\ y-(-2)=\frac{3}{4}(x-(-2)) \\ y+2=\frac{3}{4}(x+2) \end{gathered}$

D is correct.

Now, let's use the second point.

$\begin{gathered} y-y_1=m(x-x_1)_{} \\ y-1=\frac{3}{4}(x-2) \end{gathered}$

A is also correct.

Therefore, the right answers are A and D.