Algebra Practice Test

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Question: 1 / 400

What is the equation of a line that passes through the points (1,2) and (3,4)?

y = 2x + 1

y = x + 2

y = x + 1

To find the equation of a line that passes through the points (1, 2) and (3, 4), we first need to determine the slope of the line. The slope (m) can be calculated using the formula:

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

Substituting the given points (1, 2) as (x₁, y₁) and (3, 4) as (x₂, y₂):

\[ m = \frac{4 - 2}{3 - 1} = \frac{2}{2} = 1 \]

Now that we know the slope is 1, we can use the point-slope form of the equation of a line, which is given by:

\[ y - y_1 = m(x - x_1) \]

Using the point (1, 2):

\[ y - 2 = 1(x - 1) \]

Simplifying this, we add 2 to both sides:

\[ y = x - 1 + 2 \]

\[ y = x + 1 \]

This matches the equation given in the choice labeled

Get further explanation with Examzify DeepDiveBeta

y = 3x - 1

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