1. Which of the following is the equation of the line in point-slope form? A) y+y=-(1)/(3)(x-y) B) y-y=-(1)/(3)(x+y) C) y-2=(3)/(3)(x+4) D) y+2=(-3)/(4)(x-4) 2. Which of the following is the duation of theline ir slope-intercept form? A) y=(-3)/(y) x+1 (B) y=-3 x-1 c) y=-(4)/(2) x+1 D) y=-(9)/(2) x-1

Question

1. Which of the following is the equation of the line in point-slope form? A) y+y=-(1)/(3)(x-y) B) y-y=-(1)/(3)(x+y) C) y-2=(3)/(3)(x+4) D) y+2=(-3)/(4)(x-4) 2. Which of the following is the duation of theline ir slope-intercept form? A) y=(-3)/(y) x+1 (B) y=-3 x-1 c) y=-(4)/(2) x+1 D) y=-(9)/(2) x-1

Answer 1

Let's address each question one by one.1. **Equation of the line in point-slope form:**The point-slope form of a line is given by the equation:

where

is the slope and \((x_1, y_1)\) is a point on the line.Let's analyze the options:A) \( y+y=-\frac{1}{3}(x-y) \) B) \( y-y=-\frac{1}{3}(x+y) \) C) \( y-2=\frac{3}{3}(x+4) \) D) \( y+2=\frac{-3}{4}(x-4) \) Option C can be simplified to:

This matches the point-slope form with

,

, and

.Therefore, the correct answer for the first question is **C**.2. **Equation of the line in slope-intercept form:**The slope-intercept form of a line is given by the equation:

where

is the slope and

is the y-intercept.Let's analyze the options:A)

B)

C)

D)

Option B is already in the slope-intercept form with

and

.Therefore, the correct answer for the second question is **B**.

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