An equation of the line that contains the origin and the point (1,2) is

Solution:

Given, the points are (0, 0) and (1, 2)

We have to find the equation of the line that passes through the given points.

The equation of the line passing through two points is given by

\(\frac{y-y_{1}}{y_{2}-y_{1}}=\frac{x-x_{1}}{x_{2}-x_{1}}\)

Here, (x₁, y₁) = (0, 0) and (x₂, y₂) = (1, 2)

\(\frac{y-0}{2-0}=\frac{x-0}{1-0}\\\frac{y}{2}=\frac{x}{1}\)

y = 2x

Therefore, the equation of the line is y = 2x.

Example: An equation of the line that contains the origin and the point (1,3) is

Solution:

Given, the points are (0, 0) and (1, 3)

We have to find the equation of the line that passes through the given points.

The equation of the line passing through two points is given by

\(\frac{y-y_{1}}{y_{2}-y_{1}}=\frac{x-x_{1}}{x_{2}-x_{1}}\)

Here, (x₁, y₁) = (0, 0) and (x₂, y₂) = (1, 3)

\(\frac{y-0}{3-0}=\frac{x-0}{1-0}\\\frac{y}{3}=\frac{x}{1}\)

y = 3x

Therefore, the equation of the line is y = 3x.

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An equation of the line that contains the origin and the point (1,2) is

Summary:

An equation of the line that contains the origin and the point (1,2) is y = 2x.