Question

find the y -intercept of y = 3x + 7. options: 1, 0, 7, 3

Explanation:

Step1: Recall slope - intercept form

The slope - intercept form of a linear equation 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 \(b\) in the given equation

The given equation is \(y=3x + 7\). Comparing it with the slope - intercept form \(y=mx + b\), we can see that \(m = 3\) (the slope) and \(b = 7\) (the \(y\) - intercept). We can also verify this by setting \(x = 0\) in the equation: when \(x = 0\), \(y=3(0)+7=7\).

Answer:

7 (corresponding to the option with the number 7)