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

Answer 1

Slope (gradient) is #-1/3#

Slope (proper name is gradient) is the amount of change up or down for a given amount of change along.

These numbers are viewed reading from left to right.

If the slope is positive that the gradient is upwards. If the slope is negative then the gradient is downwards.

Let #P# be any point on the line
#P_1->(x_1,y_1)->(4,-1)# #P_2->(x_2,y_2)->(-5,2)#
Gradient #-> ("change in y-axis")/("change in x-axis")#
#"Gradient "-> (y_2-y_1)/(x_2-x_1)->(2-(-1))/(-5-4) = 3/(-9) = -1/3 #

The gradient is negative so the slope is downwards reading left to right.

So for 3 along you go down 1. Rather like the downward slope of a hill.

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Answer 2

To find the slope of a line passing through two points (x1, y1) and (x2, y2), you can use the formula:

Slope (m) = (y2 - y1) / (x2 - x1)

Using the given points (4, -1) and (-5, 2):

m = (2 - (-1)) / (-5 - 4) m = (2 + 1) / (-5 - 4) m = 3 / (-9) m = -1/3

Therefore, the slope of the line passing through the points (4, -1) and (-5, 2) is -1/3.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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