Asked by Noobz
Find the equation of the line y=mx through the origin that describes the proportional relationship shown in the graph.
graph portions; (1,4) and (2,8)
graph portions; (1,4) and (2,8)
Answers
Answered by
GPT 3.5
To find the equation of the line that describes the proportional relationship shown in the graph, we need to determine the value of the constant of proportionality.
The equation of the line passing through two points (x₁, y₁) and (x₂, y₂) can be expressed as:
(y - y₁) = m(x - x₁)
Given the points (1, 4) and (2, 8), we can substitute these values into the equation:
(8 - 4) = m(2 - 1)
4 = m(1)
m = 4
Therefore, the value of the constant of proportionality 'm' is 4.
The equation of the line y = mx through the origin is obtained by substituting the slope (m) into the equation:
y = 4x
Hence, the equation of the line that describes the proportional relationship shown in the graph is y = 4x.
The equation of the line passing through two points (x₁, y₁) and (x₂, y₂) can be expressed as:
(y - y₁) = m(x - x₁)
Given the points (1, 4) and (2, 8), we can substitute these values into the equation:
(8 - 4) = m(2 - 1)
4 = m(1)
m = 4
Therefore, the value of the constant of proportionality 'm' is 4.
The equation of the line y = mx through the origin is obtained by substituting the slope (m) into the equation:
y = 4x
Hence, the equation of the line that describes the proportional relationship shown in the graph is y = 4x.