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Question: 1 / 400

What is the equation of a line that passes through the points (2,3) and (4,7)?

y = 2x + 2

y = 2x + 1

To determine the equation of the line passing through the points (2,3) and (4,7), we first need to find the slope of the line using the formula for slope:

\[

m = \frac{y_2 - y_1}{x_2 - x_1}

\]

Plugging in the coordinates of the points, where (x₁, y₁) = (2, 3) and (x₂, y₂) = (4, 7):

\[

m = \frac{7 - 3}{4 - 2} = \frac{4}{2} = 2

\]

Now that we have the slope (m = 2), we can use the point-slope form of the line equation, which is:

\[

y - y_1 = m(x - x_1)

\]

Using one of the points, say (2, 3):

\[

y - 3 = 2(x - 2)

\]

Expanding this, we get:

\[

y - 3 = 2x - 4

\]

\[

y = 2x - 4 + 3

\]

\

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y = 3x - 1

y = x + 4

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