Questions: Write the equation for the relationship shown in the graph.

Solution Steps

The line passes through the points (0, 0) and (5, 20).

The slope of the line is given by the formula:

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

Using the two points (0, 0) and (5, 20), we have:

\(m = \frac{20 - 0}{5 - 0} = \frac{20}{5} = 4\)

The y-intercept is the value of y when x = 0. In this case, the line passes through the origin (0, 0), so the y-intercept is 0.

The slope-intercept form of a linear equation is:

\(y = mx + b\)

Where m is the slope and b is the y-intercept. We found that the slope \(m = 4\) and the y-intercept \(b = 0\). Substituting these values, we get:

\(y = 4x + 0\)

Simplifying, we have:

\(y = 4x\)

Final Answer