1. Problem: Find the equation of the line passing through points (1,2) and (3,6). Step 1: Calculate the slope $m = \frac{6-2}{3-1} = \frac{4}{2} = 2$. Step 2: Use point-slope form $y - y_1 = m(x - x_1)$ with point (1,2): $$y - 2 = 2(x - 1)$$ Step 3: Simplify to slope-intercept form: $$y = 2x - 2 + 2 = 2x$$ 2. Problem: Find the line with slope -1 passing through (4,3). Step 1: Point-slope form: $$y - 3 = -1(x - 4)$$ Step 2: Simplify: $$y = -x + 4 + 3 = -x + 7$$ 3. Problem: Determine the equation of the line with y-intercept 5 and slope 0.5. Step 1: Slope-intercept form: $$y = 0.5x + 5$$ 4. Problem: Find the equation of the horizontal line through (2, -3). Step 1: Horizontal line means slope $m=0$, so: $$y = -3$$ 5. Problem: Find the equation of the vertical line through $x=7$. Step 1: Vertical lines have undefined slope, equation: $$x = 7$$ 6. Problem: Find the equation of the line passing through (0,0) with slope 3. Step 1: Slope-intercept form: $$y = 3x$$ 7. Problem: Equation of a line passing through (-1,-1) and (2,4). Step 1: Compute the slope: $$m = \frac{4 - (-1)}{2 - (-1)} = \frac{5}{3}$$ Step 2: Point-slope form using (-1,-1): $$y + 1 = \frac{5}{3}(x + 1)$$ Step 3: Simplify: $$y = \frac{5}{3}x + \frac{5}{3} - 1 = \frac{5}{3}x + \frac{2}{3}$$ 8. Problem: Find the line with slope 4 that passes through (3,5). Step 1: Point-slope form: $$y - 5 = 4(x - 3)$$ Step 2: Simplify: $$y = 4x - 12 + 5 = 4x - 7$$ 9. Problem: Find slope and equation of the line passing through points (6,2) and (6,8). Step 1: The vertical line has undefined slope. Step 2: Equation: $$x = 6$$ 10. Problem: Find the equation of the line passing through (2, 3) with slope $ -2$. Step 1: Point-slope form: $$y - 3 = -2(x - 2)$$ Step 2: Simplify: $$y = -2x + 4 + 3 = -2x + 7$$