Question
The graph shows the proportional relationship. Derive the equation of the line y=mx through the origin.
(1 point)
Answers
GPT 3.5
To derive the equation of a line in slope-intercept form, we need to find the slope of the line, m, which is given by the ratio of the change in y-values to the change in x-values between two points on the line.
Since the line passes through the origin, one of the points we can use is the origin (0,0) and another point on the line (x, y).
So, let's choose a point on the line, (x, y), where x and y are coordinates of a point on the line.
The slope, m, is given by:
m = (y - 0) / (x - 0) = y/x
Therefore, y = mx
This equation represents a line passing through the origin with a slope of m.
Since the line passes through the origin, one of the points we can use is the origin (0,0) and another point on the line (x, y).
So, let's choose a point on the line, (x, y), where x and y are coordinates of a point on the line.
The slope, m, is given by:
m = (y - 0) / (x - 0) = y/x
Therefore, y = mx
This equation represents a line passing through the origin with a slope of m.