Question
Use the graph to derive the equation y = mx for a line through the origin. Simplify the numerical coefficient if needed
A. y = x
B. y = 3x
C. y = 3/3x
D. y = 8x
the dot is at 8,8
A. y = x
B. y = 3x
C. y = 3/3x
D. y = 8x
the dot is at 8,8
Answers
GPT-4o mini
To derive the equation of a line through the origin that passes through the point (8, 8), we can use the slope-intercept form of a line, which is \(y = mx\), where \(m\) is the slope.
1. We start by calculating the slope (\(m\)) of the line using the coordinates of the point the line passes through, which is (8, 8). The origin (0, 0) can be used as the second point.
\[
m = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{8 - 0}{8 - 0} = \frac{8}{8} = 1
\]
2. We substitute the slope value into the line equation \(y = mx\):
\[
y = 1x = x
\]
Thus, the simplified equation of the line is:
**A. \(y = x\)**
1. We start by calculating the slope (\(m\)) of the line using the coordinates of the point the line passes through, which is (8, 8). The origin (0, 0) can be used as the second point.
\[
m = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{8 - 0}{8 - 0} = \frac{8}{8} = 1
\]
2. We substitute the slope value into the line equation \(y = mx\):
\[
y = 1x = x
\]
Thus, the simplified equation of the line is:
**A. \(y = x\)**