Write an equation of the line through the given points. \( \begin{array}{ll}\text { 21.) }(5,1)(0,2) & 22 .)(-2,-3)(4,3)\end{array} \)

To find the equation of the line given the points, we first determine the slope \(m\). For the points (5,1) and (0,2): The slope \(m\) is calculated as: \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - 1}{0 - 5} = \frac{1}{-5} = -\frac{1}{5} \] Using point-slope form \(y - y_1 = m(x - x_1)\) with point (5,1): \[ y - 1 = -\frac{1}{5}(x - 5) \] This simplifies to: \[ y - 1 = -\frac{1}{5}x + 1 \implies y = -\frac{1}{5}x + 2 \] For the points (-2,-3) and (4,3): The slope \(m\) is: \[ m = \frac{3 - (-3)}{4 - (-2)} = \frac{6}{6} = 1 \] Using point-slope form with point (-2,-3): \[ y + 3 = 1(x + 2) \] This simplifies to: \[ y + 3 = x + 2 \implies y = x - 1 \] Thus, the equations of the lines are: 1. \(y = -\frac{1}{5}x + 2\) 2. \(y = x - 1\)