The slope of the line containing the points (-2,3) and (-3,1) is?

Solution:

If two points (x₁ , y₁) and (x₂ , y₂) lie on a straight line the equation of the line is given by either of the following equations:

y - y₁ = m(x - x₁)----------->(1)

Or

y - y₂ = m(x - x₂)----------->(2)

m in the above equations is known as the slope of the line and is calculated as follows:

m = (y₂ - y₁) / (x₂ - x₁)

In the given problem:

x₁ = -2,  y₁= 3

x₂ = -3   y₂= 1

Slope of the line m = (1 - 3) / (-3 - (-2)) = -2 / (-3+2)

= -2 / (-1)

m = 2

Using the expression (1) we get the equation:

y - 3 = m(x - (-2))

y = 2(x + 2) + 3 = 2x + 4 + 3 

y = 2x + 7  

Using the expression (2) we get the equation:

y - 1 = m(x - (-3))

y - 1 = 2(x - (-3))

y - 1 = 2x + 6

y = 2x + 7

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The slope of the line containing the points (-2,3) and (-3,1) is?

Summary:

The slope of the line containing the points (-2,3) and (-3,1) is 2.