19. a) Write an equation for the line that passes through each pair of points. Describe your strategy. i) $G(-3,-7)$ and $H(1,5)$ ii) $\mathrm{J}(-3,3)$ and $\mathrm{K}(5,-1)$ b) Use each equation you wrote in part a to determine the coordinates of another point on each line.

Step 1 ：\(\text{Find the slope: } m = \frac{5 - (-7)}{1 - (-3)} = \frac{12}{4} = 3\)

Step 2 ：\(\text{Use point-slope form: } y - 5 = 3(x - 1)\)

Step 3 ：\(\text{Simplify: } y = 3x + 2\)

Step 4 ：\(\text{Find another point: } x = 2 \Rightarrow y = 3(2) + 2 = 8 \Rightarrow (2, 8)\)

Step 5 ：\(\boxed{(2, 8)}\)

Step 6 ：\(\text{Find the slope: } m = \frac{-1 - 3}{5 - (-3)} = \frac{-4}{8} = -\frac{1}{2}\)

Step 7 ：\(\text{Use point-slope form: } y - 3 = -\frac{1}{2}(x + 3)\)

Step 8 ：\(\text{Simplify: } y = -\frac{1}{2}x + \frac{3}{2}\)

Step 9 ：\(\text{Find another point: } x = 1 \Rightarrow y = -\frac{1}{2}(1) + \frac{3}{2} = 1 \Rightarrow (1, 1)\)

Step 10 ：\(\boxed{(1, 1)}\)