Question

What is the slope of the line passing through the following points: #(–8, –6), (7,0) #?

Answer 1

gradient is`6/15`. As this is positive it means the graph 'slopes' upwards as you move from left to right.

Explanation:

The slope (proper name is gradient) is the amount of up or down for the amount of along.

Let `m` be the gradient.

`m=("Change in up or down")/("Change in amount of along")`

`color(brown)("You always measure by moving from left to right.")`

Let the first point be `" "P_1 ->(x_1,y_1) -> (-8,-6)`
Let the second point be `P_2->(x_2,y_2)->(7,0)`

Change in up or down is change in `y`

`y_("change") ->y_2-y_1" "=" "0-(-6) " "=" "0+6 " "=" "6`

Change in along is change in `x`

`x_("change")->x_2-x_1 = 7-(-8)" "=" "7+8" "=" "15`

So `" "m=(y_("change"))/(x_("change")) = 6/15`