The equation of the line through the origin parallel to y = 0.8x - 2 is y = 0.8x.
The given line has a slope of 0.8, and parallel lines share the same slope. Consequently, the slope of the required line is also 0.8.
The general equation of a line with slope
m passing through a point (x 1 ,y 1 ) is y−y1 =m(x−x 1).
In this scenario, the point (x 1 ,y 1 ) corresponds to the origin (0, 0). Substituting these values along with the slope m=0.8 into the equation, we obtain y−0=0.8(x−0).
Simplifying this expression yields y=0.8x.
Hence, the equation of the line passing through the origin and parallel to
y=0.8x−2 is y=0.8x.
This result aligns with the concept that parallel lines in a Cartesian coordinate system have the same slope.
The equation y=0.8x represents a line parallel to y=0.8x−2 but passing through the origin, as indicated by the absence of a y-intercept term.
The origin, in this case, serves as the point through which the line passes.