Question

find the y-intercept of each line defined below and compare their values.
equation of line a:
$y = \frac{2}{3}x - 2$
select values from line b:

x	y
0	2
3	1
6	0

answer attempt 1 out of 2
the y-intercept of line a is \boxed{} and the y-intercept of line b is \boxed{}. therefore the y-intercept of line a is \underline{\quad} the y-intercept of line b.

Explanation:

Step1: Find y-intercept of Line A

The equation of Line A is in slope - intercept form \(y = mx + b\), where \(b\) is the y - intercept. For the equation \(y=\frac{2}{3}x - 2\), comparing with \(y=mx + b\), we can see that \(b=- 2\). So the y - intercept of Line A is \(-2\).

Step2: Find y-intercept of Line B

The y - intercept of a line is the value of \(y\) when \(x = 0\). Looking at the table for Line B, when \(x = 0\), the corresponding \(y\) value is \(2\). So the y - intercept of Line B is \(2\).

Step3: Compare the y-intercepts

We have the y - intercept of Line A as \(-2\) and the y - intercept of Line B as \(2\). Since \(-2<2\), the y - intercept of Line A is less than the y - intercept of Line B.

Answer:

The \(y\) - intercept of Line A is \(-2\) and the \(y\) - intercept of Line B is \(2\). Therefore the \(y\) - intercept of Line A is less than the \(y\) - intercept of Line B.