Question

find the y-intercept of the line represented by the equation below.
$y = \frac{2}{5}x - 4$

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 \(b\) in the given equation

The given equation is \(y=\frac{2}{5}x - 4\). Comparing it with \(y=mx + b\), we can see that \(m=\frac{2}{5}\) and \(b=- 4\). The \(y\) - intercept is the value of \(y\) when \(x = 0\). If we substitute \(x = 0\) into the equation \(y=\frac{2}{5}(0)-4\), we get \(y=-4\). So the \(y\) - intercept is the point \((0,-4)\), and the \(y\) - intercept value (the \(y\) - coordinate when \(x = 0\)) is \(-4\).

Answer:

The \(y\) - intercept is \(-4\) (or the point \((0, - 4)\))