1.
[tex]y = -\frac{5}{7}x + 1\\a = -\frac{5}{7}\\\\A(21 , \frac{9}{2}) \\y = ax + b\\y = -\frac{5}{7}x + b\\\frac{9}{2} = -\frac{5}{7} * 21 + b\\\frac{9}{2} = -15 + b\\\frac{39}{2} = b\\b = 19\frac{1}{2} \\\\y = -\frac{5}{7}x + 19\frac{1}{2}[/tex]
2.
[tex]y = - 1\frac{2}{5}x + \frac{2}{5} \\a = -1\frac{2}{5} \\\\P(-14,5)\\y = ax + b\\y = -1\frac{2}{5}x + b\\5 = -1\frac{2}{5} * (-14) + b\\5 = 19\frac{3}{5} + b\\b = -14\frac{3}{5}\\\\y = -1\frac{2}{5}x - 14\frac{3}{5}[/tex]
3.
[tex]A(3,4)\\B(-2,1)\\\\y = ax + b\\\\\left \{ {{4 = 3a + b} \atop {1 = -2a + b}} \right. \\\left \{ {{b = 4 - 3a} \atop {1 = -2a + (4 - 3a)}} \right. \\\left \{ {{b = 4 - 3a} \atop {1 = -5a + 4}} \right. \\\left \{ {{b = 4 - 3a} \atop {-3 = -5a}} \right. \\\left \{ {{b = 4 - 3a} \atop {a = \frac{3}{5} }} \right. \\\left \{ {{b = 4 - 3*(\frac{3}{5})} \atop {a = \frac{3}{5}}} \right. \\\\\left \{ {{b = 4 - \frac{9}{5}} \atop {a = \frac{3}{5}}} \right. \\\\\\[/tex]
[tex]\left \{ {{b = \frac{11}{5}} \atop {a = \frac{3}{5}}} \right.\\\\\\y = \frac{3}{5}x + \frac{11}{5}[/tex]
