Considering the definition of a line, the equation of the line that passes through the point (-4, -6) and has a slope of 5 is y= 5x + 14.
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.
In this case, you know:
The line has a slope of 5.
The line passes through the point (-4, -6).
Substituting the value of the slope m and the value of the point in the expression of a linear equation, y = mx + b, the value of the ordinate to the origin b can be obtained:
-6= 5×(-4) + b
-6= -20 + b
-6 +20 = b
14= b
Finally, the equation of the line that passes through the point (-4, -6) and has a slope of 5 is y= 5x + 14.