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 Slopes of parallel and perpendicular lines Parallel lines have the same slope. Line a constains the points (-1,4) and (4,6). Line b contains the points (5,2) and (-3,-3). Are the two lines parallel? Step 1 is to calculate the slope for Line a. The formula for the slope of a line is: $\frac{y_2-y_1}{x_2-x_1}$ $\frac{y_2-y_1}{x_2-x_1}=\frac{6-4}{4-(-1)}=\frac{2}{5}$ Step 2 is to calculate the slope for Line b. The formula for the slope of a line is: $\frac{y_2-y_1}{x_2-x_1}$ $\frac{y_2-y_1}{x_2-x_1}=\frac{-3-2}{-3-5}=\frac{-5}{-8}=\frac{5}{8}$ Parallel lines have the same slope. Since the slope of Line a does not equal the slope of Line b, the lines cannot be parallel. Two lines are perpendicular if the slope of one line (m) equals the negative reciprocal of the other $(\frac{-1}{m})$ Line a constains the points (-2,-2) and (6,4). Line b contains the points (0,4) and (3,0). Are the two lines perpendicular? Step 1 is to calculate the slope for Line a. The formula for the slope of a line is: $\frac{y_2-y_1}{x_2-x_1}$ $\frac{y_2-y_1}{x_2-x_1}=\frac{4-(-2)}{6-(-2)}=\frac{4+2}{6+2}=\frac{6}{8}=\frac{3}{4}$ Step 2 is to calculate the slope for Line b. The formula for the slope of a line is: $\frac{y_2-y_1}{x_2-x_1}$ $\frac{y_2-y_1}{x_2-x_1}=\frac{0-4}{3-0}=\frac{-4}{3}$ Two lines are perpendicular if the slope of one line (m) equals the negative reciprocal of the other $(\frac{-1}{m})$. Since the slope of Line a is 3/4 and the slope of Line b is -4/3, the lines are perpendicular.