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

Let's address each question one by one.<br /><br />1. **Equation of the line in point-slope form:**<br /><br />The point-slope form of a line is given by the equation:<br />\[ y - y_1 = m(x - x_1) \]<br />where \( m \) is the slope and \((x_1, y_1)\) is a point on the line.<br /><br />Let's analyze the options:<br /><br />A) \( y+y=-\frac{1}{3}(x-y) \) <br />B) \( y-y=-\frac{1}{3}(x+y) \) <br />C) \( y-2=\frac{3}{3}(x+4) \) <br />D) \( y+2=\frac{-3}{4}(x-4) \) <br /><br />Option C can be simplified to:<br />\[ y - 2 = 1(x + 4) \]<br />This matches the point-slope form with \( m = 1 \), \( x_1 = -4 \), and \( y_1 = 2 \).<br /><br />Therefore, the correct answer for the first question is **C**.<br /><br />2. **Equation of the line in slope-intercept form:**<br /><br />The slope-intercept form of a line is given by the equation:<br />\[ y = mx + b \]<br />where \( m \) is the slope and \( b \) is the y-intercept.<br /><br />Let's analyze the options:<br /><br />A) \( y=\frac{-3}{y} x+1 \) <br />B) \( y=-3x-1 \) <br />C) \( y=-\frac{4}{2}x+1 \) <br />D) \( y=-\frac{9}{2}x-1 \) <br /><br />Option B is already in the slope-intercept form with \( m = -3 \) and \( b = -1 \).<br /><br />Therefore, the correct answer for the second question is **B**.