Final answer:
To find an equation of a line parallel to the one through (0,0) and (-2, 6), first determine the slope (-3) and then use the point-slope form with a point on the new line. If the new line also passes through (0,0), the equation is y = -3x.
Step-by-step explanation:
To create an equation for a line that is parallel to the one passing through the given points (0,0) and (-2, 6), we first need to determine the slope of the line through these points. The slope of a line is calculated by the change in y over the change in x (rise over run) using the formula:
slope (m) = (y2 - y1) / (x2 - x1)
Substituting our points, we get:
m = (6 - 0) / (-2 - 0) = 6 / -2 = -3
Since parallel lines have equal slopes, the slope of the new line is also -3. Now, we can use the point-slope form to create the equation of the line, which is:
y - y1 = m(x - x1)
To form the equation, we can use any point through which we want our parallel line to pass. Assuming we want our new line to pass also through the origin (0,0), we get:
y - 0 = -3(x - 0)
Therefore, the equation of the line parallel to the one through (0,0) and (-2, 6) is y = -3x.