Use the image to answer the question.

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 4 right parenthesis and left parenthesis 2 comma 8 right parenthesis.

Find the equation of the line y=mx
through the origin that describes the proportional relationship shown in the graph.

(1 point)
y=

Answer 1

To find the equation of the line in the form \(y = mx\) that passes through the origin and describes the proportional relationship based on the given points \((1, 4)\) and \((2, 8)\), we first need to determine the slope \(m\).

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

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

Using the points \((x_1, y_1) = (1, 4)\) and \((x_2, y_2) = (2, 8)\):

\[ m = \frac{8 - 4}{2 - 1} = \frac{4}{1} = 4 \]

Now that we have the slope, we can form the equation of the line through the origin:

\[ y = mx \quad \Rightarrow \quad y = 4x \]

Thus, the equation of the line is:

\[ \boxed{4x} \]