Graphing Linear Equations Unit Test

Question

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Question
Use the image to answer the question.

An illustration shows a coordinate plane with 4 quadrants. The x-axis ranges from negative 9 to 9 in one unit increments, and the y-axis ranges from negative 11 to 11 in one unit increments. A line is graphed on the plane. An upward slanting line passes through points plotted at left parenthesis 1 comma 5 right parenthesis and left parenthesis 2 comma 10 right parenthesis.

The graph shows the proportional relationship. Derive the equation of the line y=mx
through the origin.

(1 point)
y=

Answer 1

To derive the equation of the line \( y = mx \) that passes through the origin, we need to find the slope \( m \) using the two points provided: \( (1, 5) \) and \( (2, 10) \).

The slope \( m \) is calculated using the formula:

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

Substituting in our points:

\[ m = \frac{10 - 5}{2 - 1} = \frac{5}{1} = 5 \]

Now that we have the slope, we can write the equation of the line that goes through the origin (\( y = mx \)):

\[ y = 5x \]

Therefore, the derived equation of the line is:

\[ y = 5x \]