Extra Practice begins on page R4. Wroblem Solving Write an equation in point-slope form for the line that passes through each point with given slope. Then graph the equation. \( \begin{array}{lll}\text { 13. }(-6,-3), m=-1 & \text { 14. }(-7,6), m=0 & \text { 15. }(-2,11) \text {, vertical line } \\ \text { 16. }(-6,-8), m=-\frac{5}{8} & \text { 17. }(-2,-9), m=-\frac{7}{5} & \text { 18. }(-6,0) \text {, horizontal line }\end{array} \) Vrite an equation in point-slone form slone-intercept form, and standard form for eac

Let's solve each problem step by step. ### Problem 13: Point (-6, -3), Slope \( m = -1 \) **Point-Slope Form:** The point-slope form of a line is given by: \[ y - y_1 = m(x - x_1) \] Substituting the point \((-6, -3)\) and the slope \(m = -1\): \[ y - (-3) = -1(x - (-6)) \] This simplifies to: \[ y + 3 = -1(x + 6) \] **Slope-Intercept Form:** To convert to slope-intercept form \(y = mx + b\): \[ y + 3 = -x - 6 \] \[ y = -x - 9 \] **Standard Form:** To convert to standard form \(Ax + By = C\): \[ x + y = -9 \] ### Problem 14: Point (-7, 6), Slope \( m = 0 \) **Point-Slope Form:** Since the slope is \(0\), the line is horizontal: \[ y - 6 = 0(x + 7) \] This simplifies to: \[ y = 6 \] **Slope-Intercept Form:** Already in slope-intercept form: \[ y = 6 \] **Standard Form:** To convert to standard form: \[ 0x + y = 6 \quad \text{or simply} \quad y = 6 \] ### Problem 15: Point (-2, 11), Vertical Line A vertical line has an undefined slope and is represented as: \[ x = -2 \] ### Problem 16: Point (-6, -8), Slope \( m = -\frac{5}{8} \) **Point-Slope Form:** \[ y - (-8) = -\frac{5}{8}(x - (-6)) \] This simplifies to: \[ y + 8 = -\frac{5}{8}(x + 6) \] **Slope-Intercept Form:** Distributing: \[ y + 8 = -\frac{5}{8}x - \frac{30}{8} \] \[ y = -\frac{5}{8}x - \frac{30}{8} - 8 \] Converting \(-8\) to eighths: \[ y = -\frac{5}{8}x - \frac{30}{8} - \frac{64}{8} \] \[ y = -\frac{5}{8}x - \frac{94}{8} \] **Standard Form:** Multiply through by 8 to eliminate the fraction: \[ 8y = -5x - 94 \] Rearranging gives: \[ 5x + 8y = -94 \] ### Problem 17: Point (-2, -9), Slope \( m = -\frac{7}{5} \) **Point-Slope Form:** \[ y - (-9) = -\frac{7}{5}(x - (-2)) \] This simplifies to: \[ y + 9 = -\frac{7}{5}(x + 2) \] **Slope-Intercept Form:** Distributing: \[ y + 9 = -\frac{7}{5}x - \frac{14}{5} \] \[ y = -\frac{7}{5}x - \frac{14}{5} - 9 \] Converting \(-9\) to fifths: \[ y = -\frac{7}{5}x - \frac{14}{5} - \frac{45}{5} \] \[ y = -\frac{7}{5}x - \frac{59}{5} \] **Standard Form:** Multiply through by 5: \[ 5y = -7x - 59 \] Rearranging gives: \[ 7x + 5y = -59 \] ### Problem 18: Point (-6, 0), Horizontal Line A horizontal line has a slope of \(0\) and is represented as: \[ y = 0 \] ### Summary of Equations 1. **Problem 13:** - Point-Slope: \(y + 3 = -1(x + 6)\) - Slope-Intercept: \(y = -x - 9\) - Standard: \(x + y = -9\) 2. **Problem 14:** - Point-Slope: \(y = 6\) - Slope-Intercept: \(y = 6\) - Standard: \(y = 6\) 3. **Problem 15:** - Vertical Line: \(x = -2\) 4. **Problem 16:** - Point-Slope: \(y + 8 = -\frac{5}{8}(x + 6)\) - Slope-Intercept: \(y = -\frac{5}{8}x - \frac{94}{8}\) - Standard: \(5x + 8y = -94\) 5. **Problem 17:** - Point-Slope: \(y + 9 = -\frac{7}{5}(x + 2)\) - Slope-Intercept: \(y = -\frac{7}{5}x - \frac{59}{5}\) - Standard: \(7x + 5y = -59\) 6. **Problem 18:** - Horizontal Line: \(y = 0\)