The formula for find the slope of a line is:
m = (color(red)(y_2) - color(blue)(y_1))/(color(red)(x_2) - color(blue)(x_1))m=y2−y1x2−x1
Where (color(blue)(x_1), color(blue)(y_1))(x1,y1) and (color(red)(x_2), color(red)(y_2))(x2,y2) are two points on the line.
Substituting the values from the points in the problem gives:
m = (color(red)(-1/5) - color(blue)(-1))/(color(red)(-1/5) - color(blue)(7/10)) = (color(red)(-1/5) + color(blue)(1))/(color(red)(-1/5) - color(blue)(7/10)) = (color(red)(-1/5) + color(blue)(5/5))/(color(red)(-2/10) - color(blue)(7/10)) = (4/5)/(-9/10) = -40/45 = -8/9m=−15−−1−15−710=−15+1−15−710=−15+55−210−710=45−910=−4045=−89
