11) \( (-7,9),(8,1) \) Find the slope of each line. Also, find the \( y \)-intercept. \( \begin{array}{ll}\text { 13) } y=-\frac{5}{3} x & \text { 12) }(-8,12),(-8,-14) \\ \text { Sketch the graph of each line on separate graph paper using the slope-intercept method! } \\ \text { 15) } y=-\frac{8}{5} x-5 & \text { 14) } y=-\frac{1}{4} x+4\end{array} \) 16) \( y=2 x-3 \)

**Problem 11: Line Through \((-7,9)\) and \((8,1)\)** 1. To find the slope \( m \), use the formula \[ m = \frac{y_2-y_1}{x_2-x_1}. \] 2. Substitute the given points: \[ m = \frac{1-9}{8-(-7)} = \frac{-8}{15} = -\frac{8}{15}. \] 3. To find the \( y \)-intercept, use the point-slope form: \[ y - y_1 = m(x - x_1). \] Using point \((-7,9)\): \[ y - 9 = -\frac{8}{15}(x - (-7)) = -\frac{8}{15}(x+7). \] 4. Substitute \( x=0 \) to find the \( y \)-intercept: \[ y - 9 = -\frac{8}{15}(0+7) = -\frac{56}{15}. \] \[ y = 9 - \frac{56}{15}. \] 5. Express \( 9 \) as a fraction with denominator 15: \[ 9=\frac{135}{15}\quad\Longrightarrow\quad y=\frac{135}{15}-\frac{56}{15}=\frac{79}{15}. \] 6. The \( y \)-intercept is \(\left(0, \frac{79}{15}\right)\). --- **Problem 12: Line Through \((-8,12)\) and \((-8,-14)\)** 1. Use the slope formula: \[ m = \frac{-14-12}{-8-(-8)} = \frac{-26}{0}. \] 2. Since division by zero is undefined, the slope is undefined. 3. The line is vertical with equation \( x=-8 \). 4. A vertical line does not have a \( y \)-intercept (unless \( x=-8 \) equals 0, which it does not). --- **Problem 13: \( y=-\frac{5}{3}x \)** 1. The equation is in slope-intercept form \( y=mx+b \). 2. The slope is: \[ m=-\frac{5}{3}. \] 3. The \( y \)-intercept is at: \[ b=0,\quad \text{or} \quad(0,0). \] --- **Problem 14: \( y=-\frac{1}{4}x+4 \)** 1. The equation is in slope-intercept form. 2. The slope is: \[ m=-\frac{1}{4}. \] 3. The \( y \)-intercept is: \[ b=4,\quad \text{or} \quad(0,4). \] --- **Problem 15: \( y=-\frac{8}{5}x-5 \)** 1. The equation is already in slope-intercept form. 2. The slope is: \[ m=-\frac{8}{5}. \] 3. The \( y \)-intercept is: \[ b=-5,\quad \text{or} \quad(0,-5). \] --- **Problem 16: \( y=2x-3 \)** 1. The equation is in slope-intercept form. 2. The slope is: \[ m=2. \] 3. The \( y \)-intercept is: \[ b=-3,\quad \text{or} \quad(0,-3). \]