A line passes through (3, 7) and (6, 9). Which equation best represents the line?
y = 3 over 2x + 5
y = 2 over 3x + 5
y = 3x + 2
y = 2 over 3x + 2

Solution:

Given, the points are (3, 7) and (6, 9)

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) = (3, 7) and (x₂, y₂) = (6, 9)

\(\frac{y-7}{9-7}=\frac{x-3}{6-3}\\\frac{y-7}{2}=\frac{x-3}{3}\)

On cross multiplication,

3(y - 7) = 2(x - 3)

3y - 21 = 2x - 6

3y = 2x + 21 - 6

3y = 2x + 15

Dividing by 3 on both sides,

y = (2/3)x + 5

Therefore, the equation of the line is y = (2/3)x + 5.

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A line passes through (3, 7) and (6, 9). Which equation best represents the line?

Summary:

An equation of the line that passes through the given points (3, 7) and (6, 9) is y = (2/3)x + 5.