Question

Find the gradient of the line segment between the points (2,-3) and (-3,-8).

Answer 1

Concept:

The gradient of a line segment is a measure to know the steepness of the line. A line with a large gradient will be steeper and a line with zero gradients will be horizontal.

Given:

We have,

Points (2,-3) and (-3,-8).

Find:

We are asked to find the gradient of the line segment between the given points.

Solution:

So,

We have,

Points (2,-3) and (-3,-8).

i.e.

x₁ = 2, x₂ = -3

And,  

y₁ = -3,  y₂ = -8

Now,

Using the gradient formula,

i.e.

Gradient = (y₂ - y₁) / (x₂ - x₁)

So,

Now, Substituting the values of x and y in the above-mentioned formula,

We get,

Gradient = (y₂ - y₁) / (x₂ - x₁)

i.e.

Gradient = [(-8 -(-3)) / (-3 - 2)]

We get,

Gradient = [ (-8 + 3) / (-3 -2)]

i.e.

Gradient = [ -5 / -5] = 1

So,

The gradient of given point is 1.

Hence, the gradient of the line segment between the given points is 1.

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Answer 2

Answer:

The answer is -1