Suppose we are given the following. Line 1 passes through (2,-8) and (-2,2) Line 2 passes through (0,-1) and (5,6) Line 3 passes through (2,-2) and (4,-7) (a) Find the slope of each line. Slope of Line1= square Slope of Line2= square Slope of Line3= square (b) For each pair of lines determine whether they are parallel, per Line 1 and Line 2: Parallel Perpendicular Line 1 and Line 3: Oparallel Perpendicular Line 2 and Line 3: Parallel Perpendicular

(a) To find the slope of each line, we can use the formula:<br /><br />\[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \]<br /><br />For Line 1:<br />\[ \text{slope} = \frac{2 - (-8)}{-2 - 2} = \frac{10}{-4} = -\frac{5}{2} \]<br /><br />For Line 2:<br />\[ \text{slope} = \frac{6 - (-1)}{5 - 0} = \frac{7}{5} \]<br /><br />For Line 3:<br />\[ \text{slope} = \frac{-7 - (-2)}{4 - 2} = \frac{-5}{2} \]<br /><br />So, the slopes are:<br />\[ \text{Slope of Line 1} = -\frac{5}{2} \]<br />\[ \text{Slope of Line 2} = \frac{7}{5} \]<br />\[ \text{Slope of Line 3} = -\frac{5}{2} \]<br /><br />(b) To determine if the lines are parallel or perpendicular, we compare their slopes.<br /><br />Line 1 and Line 2:<br />The slopes are \(-\frac{5}{2}\) and \(\frac{7}{5}\), which are neither equal nor negative reciprocals. Therefore, they are neither parallel nor perpendicular.<br /><br />Line 1 and Line 3:<br />The slopes are \(-\frac{5}{2}\) and \(-\frac{5}{2}\), which are equal. Therefore, they are parallel.<br /><br />Line 2 and Line 3:<br />The slopes are \(\frac{7}{5}\) and \(-\frac{5}{2}\), which are neither equal nor negative reciprocals. Therefore, they are neither parallel nor perpendicular.