What is the slope of the line that passes through the points (2, 1)(2,1) and (17, -17) ?(17,−17)? in simplest form

Question

bf vutgeuw vtefqiu guyewftyi fuftiyw uo fyuewf yt ftiew f ufouew f

Answer 1

(2,1) and (17, -17) are points with a line through them that has slope = (1- -17)/(2 -17) = 18/-15 = - 6/5

slope = change in y over change in x = "rise over run" = the difference in y coordinates divided by the corresponding difference in x coordinates.

slope = -6/5 = - 1.2

you could have calculated the slope in a reverse order (-17 -1)/(17-2) = - 18/15 = -6/5 = -1.2

slope = (y1 -y2)/(x1 -x2) = (y2 -y1)/(x^2 -x1)

the equation of the line through the two given points is

(y-1)/(x-2) = -6/5

y-1 = (-6/5)(x+2) = (-6/5)x + 12/5

y = (-6/5)x +12/5 +1 = (-6/5)x +17/5

y = (-6/5)x + 17/5 in slope intercept form where the coefficient of the x term is the slope, when the equation is solved for y

y = (-1.2)x + 3.4

the line through the two points is downward sloping, due to the negative sign.

It might help to sketch the graph and plot the points

check the answer, plug in the points into the equation

for (2,1), 1 = (-1.2)(2) -+3.4 = -2.4 + 3.4 = 1

for (17, -17) -17 = (-1.2)(17) + 3.4 = -20.4 + 3.4 = -17