Find the equation of the line that goes through the origin and is parallel to the line y=−0.5x−8
(0, 0), m = -0.5.
Y = mx + b.
0 = -0.5 * 0 + b.
b = 0.
Eq: Y = -0.5x.
If it goes through the origin, its equation is
y = mx
where m is the slope.
So, what is the slope of your given line?
Or, coonsider that your line is given in the slope-intercept form, so its y-intercept is at (0,-8).
So, what would be the line with the same slope, where the y-intercept is at (0,0) ?
To find the equation of a line that is parallel to the given line and passes through the origin, we can use the fact that parallel lines have the same slope.
The given line has a slope of -0.5. So, the equation of the parallel line will also have a slope of -0.5.
The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. As the parallel line passes through the origin (0,0), the y-intercept, b, will be 0.
Therefore, the equation of the line that goes through the origin and is parallel to the line y = -0.5x - 8 is y = -0.5x.
Note that we do not include the y-intercept term (b = 0) in this case because the line passes through the origin.