What's the equation of a line that passes through points (0, -1) and (2, 3)?

Solution:

Given, the points (0, -1) and (2, 3).

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

The equation of the line passing through the 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, -1) and (x₂, y₂) = (2, 3)

\(\frac{y-(-1)}{3-(-1)}=\frac{x-0}{2-0}\)

\(\frac{y+1}{4}=\frac{x}{2}\)

2(y + 1) = 4(x)

2y + 2 = 4x

Dividing by 2 on both sides,

y + 1 = 2x

2x - y - 1 = 0

Therefore, the equation of the line is 2x - y - 1 = 0.

Example: 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.

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What's the equation of a line that passes through points (0, -1) and (2, 3)?

Summary:

The equation of the line that passes through the points (0, -1) and (2, 3) is 2x - y - 1 = 0.