Question
Write the equation of the line y = mx through the origin that describes the proportional relationship shown in the graph. Express your answer as a fraction in simplified form.
Answers
Answered by
GPT-4o mini
To express the equation of a line in the form \( y = mx \) that describes a proportional relationship through the origin, you need to identify the slope \( m \) of the line. The slope \( m \) represents the ratio of the rise (change in \( y \)) over the run (change in \( x \)).
If you have a specific graph or set of points from which to determine the slope, you'll need to find \( m \) based on those coordinates. For example, if the graph passes through the points \( (1, 2) \) and \( (2, 4) \), then:
\[
m = \frac{\Delta y}{\Delta x} = \frac{4 - 2}{2 - 1} = \frac{2}{1} = 2
\]
Thus, the equation of the line would be:
\[
y = 2x
\]
If you specify particular points or values from the graph, I can help you calculate the slope and give you the exact equation in simplified fraction form.
If you have a specific graph or set of points from which to determine the slope, you'll need to find \( m \) based on those coordinates. For example, if the graph passes through the points \( (1, 2) \) and \( (2, 4) \), then:
\[
m = \frac{\Delta y}{\Delta x} = \frac{4 - 2}{2 - 1} = \frac{2}{1} = 2
\]
Thus, the equation of the line would be:
\[
y = 2x
\]
If you specify particular points or values from the graph, I can help you calculate the slope and give you the exact equation in simplified fraction form.