The equation of the line y=mx through the origin represents a proportional relationship between x and y, where m is the constant of proportionality (slope). In this case, the equation of the line through the origin in the graph is y = 3x.
Therefore, the equation of the line that describes the proportional relationship in the graph is y = 3x.
Find the equation of the line y=mx through the origin that describes the proportional relationship shown in the graph. What’s the answer
3 answers
An illustration shows a graph labeled Football Cost. The horizontal axis is labeled Quantity and ranges from 0 to 5 in increments of 1. The vertical axis is labeled Cost and ranges from 0 to 39 in increments of 3. An upward slanting line segment connects points plotted at left parenthesis 0 comma 0 right parenthesis, left parenthesis 1 comma 9 right parenthesis, left parenthesis 2 comma 18 right parenthesis, left parenthesis 3 comma 27 right parenthesis, and left parenthesis 4 comma 36 right parenthesis. The price for footballs is displayed in the graph. Derive the equation of the proportional relationship through the origin. What’s the answer
To find the equation of the proportional relationship through the origin, we need to determine the slope of the line connecting the point (0,0) and (1,9) on the graph.
The slope (m) of a line passing through two points (x₁, y₁) and (x₂, y₂) is given by the formula:
m = (y₂ - y₁) / (x₂ - x₁)
For the given points (0,0) and (1,9), we have:
m = (9 - 0) / (1 - 0) = 9
So, the equation of the line representing the proportional relationship through the origin is:
y = 9x
Therefore, the answer is y = 9x.
The slope (m) of a line passing through two points (x₁, y₁) and (x₂, y₂) is given by the formula:
m = (y₂ - y₁) / (x₂ - x₁)
For the given points (0,0) and (1,9), we have:
m = (9 - 0) / (1 - 0) = 9
So, the equation of the line representing the proportional relationship through the origin is:
y = 9x
Therefore, the answer is y = 9x.