Question

find the y-intercept of the line represented by the equation below.
$y = -4 - \frac{2}{3}x$

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: Rewrite the given equation

The given equation is \(y=-4-\frac{2}{3}x\). We can rewrite it in the form \(y = mx + b\) as \(y=-\frac{2}{3}x-4\).
By comparing with \(y = mx + b\), we can see that \(b=-4\). The \(y\) - intercept is the value of \(y\) when \(x = 0\). If we substitute \(x = 0\) into the equation \(y=-4-\frac{2}{3}x\), we get \(y=-4-\frac{2}{3}(0)=-4\).

Answer:

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