Considering the expression of a line, the equation of the line that passes through the pair of points (-5,-11) and (6,11) is y=2x -1.
Linear equation
A linear equation o line can be expressed in the form y = mx + b
where
- x and y are coordinates of a point.
- m is the slope.
- b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.
Knowing two points (x₁, y₁) and (x₂, y₂) of a line, the slope m of said line can be calculated using:
m= (y₂ - y₁)÷ (x₂ - x₁)
Substituting the value of the slope m and the value of one of the points in the expression y = mx + b, the value of the ordinate to the origin b can be obtained.
Equation in this case
In this case, being (x₁, y₁)= (-5, -11) and (x₂, y₂)= (6,11), the slope m can be calculated as:
m= (11 - (-11))÷ (6 - (-5))
m= (11 +11)÷ (6 + 5)
m= 22÷ 11
m= 2
Considering point 2 and the slope m, you obtain:
11= 2×6 + b
11= 12 +b
11 -12= b
-1= b
Finally, the equation of the line is y=2x -1.
Learn more about the equation of a line having 2 points:
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