Question

which are equations of the given line in point slope form? select all that apply.

□ ( y + 2 = -(x - 3) )
□ ( y + 1 = -(x - 2) )
□ ( y = x - 1 )
□ ( x - y = 1 )
□ ( y + 2 = -(x + 3) )

Explanation:

Step1: Find line slope

Pick two points on line, e.g., $(0,0)$ and $(1,-1)$.
Slope $m=\frac{-1-0}{1-0}=-1$

Step2: Recall point-slope form

Point-slope formula: $y-y_1=m(x-x_1)$

Step3: Test option E

Use point $(-3,-2)$: $y-(-2)=-1(x-(-3))$, simplifies to $y+2=-(x+3)$

Step4: Eliminate other options

• Option A: Slope is -1, but $(3,-2)$ is not on the line.
• Option B: Slope is -1, but $(2,-1)$ is not on the line.
• Option C: This is slope-intercept form, not point-slope.
• Option D: This is standard form, not point-slope.

Answer:

E. $y+2=-(x+3)$