What is the slope of the line passing through the following points: #(-1, -2), (4,-5)#?

1 Answer
Tony B
Mar 21, 2016

Slope (gradient )#-> -3/5#

Explanation:

Slope (gradient) is the amount of up or down for the amount of along. Like the incline on a hill.

Always read from left to right. If you go up reading left to right then it is a positive gradient. If you go down reading left to right then it is a negative gradient.

Gradient# ->("change in y-axis")/("change in x-axis")#

A memory jog could be "Why is this one on top".

Let Point 1#->P_1->(x_1,y_1)->(-1,-2)#

Let Point 2#->P_2->(x_2,y_2)->(4,-5)#

Let gradient be #m#

Gradient#color(white)(.)(m) ->("change in y-axis")/("change in x-axis")->(y_2 - y_1)/(x_2-x_1)#

#m=(-5-(-2))/(4-(-1)) = (-3)/5 = -3/5#

This is negative so for 5 along it goes down 3.

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