Question

find the y-intercept of the line represented by the equation below.
$y = -\frac{3}{5}x + 2$

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. The y - intercept is the value of \(y\) when \(x = 0\).

Step2: Identify the y - intercept from the equation

Given the equation \(y=-\frac{3}{5}x + 2\), comparing it with the slope - intercept form \(y=mx + b\), we can see that when \(x = 0\), \(y=b\). Here, \(b = 2\). We can also verify this by substituting \(x = 0\) into the equation:
Substitute \(x = 0\) into \(y=-\frac{3}{5}x+2\), we get \(y=-\frac{3}{5}(0)+2=0 + 2=2\).

Answer:

The y - intercept is \(2\) (or the point \((0,2)\)).