1. Problem: Find the slope of the line through points (1, 3) and (4, 9). Step 1: Use the slope formula $$m = \frac{y_2 - y_1}{x_2 - x_1}$$. Step 2: Substitute the points: $$m = \frac{9 - 3}{4 - 1} = \frac{6}{3} = 2$$. 2. Problem: Find the slope of the line through points (2, 5) and (6, 13). Step 1: Use the slope formula $$m = \frac{y_2 - y_1}{x_2 - x_1}$$. Step 2: Substitute the points: $$m = \frac{13 - 5}{6 - 2} = \frac{8}{4} = 2$$. 3. Problem: Find the slope of the line given by the equation $$y = -2x + 5$$. Step 1: Recognize the slope-intercept form of a line $$y = mx + b$$. Step 2: Identify the slope $$m = -2$$. 4. Problem: For Table A (x: 0,1,2,3; y: 2,5,8,11) and Equation B $$y=4x+1$$, find slope and y-intercept, then compare. Table A: Step 1: Calculate slope using two points, e.g., (0,2) and (1,5): $$m = \frac{5 - 2}{1 - 0} = 3$$. Step 2: The y-intercept is when $$x=0$$, so $$y=2$$. Equation B: Step 1: The slope is the coefficient of $$x$$, $$m=4$$. Step 2: The y-intercept is $$b=1$$. Comparison: - Slope Table A: $$3$$, Equation B: $$4$$. So, Equation B increases faster. - Y-intercept Table A: $$2$$, Equation B: $$1$$. So, Table A starts higher.