How do you find the slope of (1,5), (-8,2)?

2 Answers
Jun 28, 2016

Slope = 1/3

Explanation:

To find the slope for any 2 points (x_1,y_1) and (x_2, y_2), you use the following formula:

slope formula: m = [y_1 - y_2] / [x_1 - x_2]

For our case, points are (1,5) and (-8,2)

slope m = (5-2)/(1-(-8)) = 3/9 = 1/3

Jun 28, 2016

The gradient (slope) is 1/3

Explanation:

Like the gradient on a hill, the slope (gradient) is the amount of change in the up or down for the given amount of along as you read from left to right.

Let the gradient be m

m=("change in up or down")/("change in along")->("change in y")/("change in x")

I have reversed the order of your points so that the x values read left to right.

Let the first point be " "P_1->(x_1,y_1)=(color(brown)(-8,2))
Let the second point be P_2->(x_2,y_2)=(color(blue)(1,5))

m=(color(blue)(y_2)color(brown)(-y_1))/(color(blue)(x_2)color(brown)(-x_1)) = color(brown)(color(blue)(5)-2)/(color(blue)(1)color(brown)(-(-8)))

But 1-(-8) is the same as 1+8
Note that 2 minuses is the same as a plus.

m=(5-2)/(1+8)=3/9

But 3/9-=(3-:3)/(9-:3)-=1/3

So the gradient (slope) is 1/3

This means that if you move to the right by 3 you have gone up 1
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
color(blue)("Additional Teaching bit")
Suppose the gradient had been -1/3

This would mean that you go to the right by 3 but you go down 1.

Negative gradient is a downward slope ( left to right)
Positive gradient is an upward slop (left to right)