1. **Find the slope of the line through (2, 3) and (5, 9).** The slope formula is $$m = \frac{y_2 - y_1}{x_2 - x_1}$$. Substitute points: $$m = \frac{9 - 3}{5 - 2} = \frac{6}{3} = 2$$. 2. **Find the x- and y-intercepts of the line 2x + 3y = 12.** For y-intercept, set $$x=0$$: $$3y = 12 \Rightarrow y = 4$$, so y-intercept is $$(0,4)$$. For x-intercept, set $$y=0$$: $$2x = 12 \Rightarrow x = 6$$, so x-intercept is $$(6,0)$$. 3. **Write the equation of a line with slope 2 and y-intercept -3.** Using slope-intercept form $$y = mx + b$$, substitute $$m=2$$ and $$b=-3$$: $$y = 2x - 3$$. 4. **Find the slope of the line 4x - 2y = 8.** Rewrite in slope-intercept form: $$4x - 2y = 8 \Rightarrow -2y = -4x + 8 \Rightarrow y = 2x - 4$$. Slope $$m = 2$$. 5. **Find the equation of the line through (0, 5) and (4, 9).** Calculate slope: $$m = \frac{9 - 5}{4 - 0} = \frac{4}{4} = 1$$. Using point-slope form with point (0,5): $$y = mx + b \Rightarrow 5 = 1 \times 0 + b \Rightarrow b = 5$$. Equation: $$y = x + 5$$. 6. **Determine if lines 2x + y = 3 and 4x + 2y = 6 are parallel, perpendicular, or same.** Rewrite first line: $$y = -2x + 3$$. Rewrite second line: $$2y = -4x + 6 \Rightarrow y = -2x + 3$$. Both have same slope and intercept, so they are the same line (coincident). 7. **Find the line parallel to y = 3x + 2 through (-1, 4).** Parallel lines have same slope $$m=3$$. Use point-slope form: $$y - 4 = 3(x + 1) \Rightarrow y = 3x + 3 + 4 = 3x + 7$$. 8. **Find the line perpendicular to y = \frac{1}{2}x + 1 passing through (2, 0).** Perpendicular slope is negative reciprocal: $$m = -2$$. Use point-slope form: $$y - 0 = -2(x - 2) \Rightarrow y = -2x + 4$$. 9. **Find the distance between A(1, 2) and B(4, 6).** Distance formula: $$d = \sqrt{(4 - 1)^2 + (6 - 2)^2} = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = 5$$. 10. **Find the midpoint of (-2, 4) and (6, 8).** Midpoint formula: $$M = \left( \frac{-2 + 6}{2}, \frac{4 + 8}{2} \right) = (2, 6)$$. **Final answers:** 1. $$m=2$$ 2. x-intercept $$(6,0)$$, y-intercept $$(0,4)$$ 3. $$y=2x-3$$ 4. $$m=2$$ 5. $$y=x+5$$ 6. Same line (coincident) 7. $$y=3x+7$$ 8. $$y=-2x+4$$ 9. $$5$$ 10. $$(2,6)$$