Question

write the equation of the line in fully simplified slope - intercept form.

Explanation:

Step1: Recall slope-intercept form

The slope - intercept form of a line is \(y = mx + b\), where \(m\) is the slope and \(b\) is the \(y\) - intercept.

Step2: Identify the slope (\(m\)) and \(y\) - intercept (\(b\))

From the given information, the slope \(m=\frac{1}{5}\) (since \(\frac{1}{5}\) is calculated as the slope) and the \(y\) - intercept \(b = 2\) (the value of \(y\) when \(x = 0\)).

Step3: Substitute \(m\) and \(b\) into the slope - intercept form

Substitute \(m=\frac{1}{5}\) and \(b = 2\) into \(y=mx + b\). We get \(y=\frac{1}{5}x+2\).

Answer:

\(y=\frac{1}{5}x + 2\)