Considering the expression of a line, the equation of the line that passes through the pair of points (-2,-6) and (-8,0) is y=-1x -8.
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)= (-2, -6) and (x₂, y₂)= (-8,0), the slope m can be calculated as:
m= (0 - (-6))÷ (-8 - (-2))
m= (0 +6)÷ (-8 +2)
m= 6÷ (-6)
m= -1
Considering point 2 and the slope m, you obtain:
0= -1×(-8) + b
0= 8 +b
0 -8= b
-8= b
Finally, the equation of the line is y=-1x -8.