Question

fill in the blanks with the appropriate responses. the line ( x + 2 = 0 ) has ( x )-intercept ____. it __ have a ( y )-intercept. the slope of this line is __. the line ( 4y = 2 ) has ( y )-intercept __. it __ have an ( x )-intercept. the slope of this line is ____.

Explanation:

Step1: Analyze the line \( x + 2 = 0 \) (rewrite as \( x=-2 \))

For x - intercept: The x - intercept is the value of x when y = 0. For the line \( x=-2 \), when y = 0, x=-2. So the x - intercept is - 2.
For y - intercept: The y - intercept is the value of y when x = 0. But for the line \( x=-2 \), x is always - 2, so there is no y - intercept (because x can never be 0). So it does not have a y - intercept.
For slope: The line \( x=-2 \) is a vertical line. The slope of a vertical line is undefined.

Step2: Analyze the line \( 4y = 2 \) (rewrite as \( y=\frac{2}{4}=\frac{1}{2} \))

For y - intercept: The y - intercept is the value of y when x = 0. For the line \( y = \frac{1}{2}\), when x = 0, y=\(\frac{1}{2}\). So the y - intercept is \(\frac{1}{2}\).
For x - intercept: The x - intercept is the value of x when y = 0. But for the line \( y=\frac{1}{2}\), y is always \(\frac{1}{2}\), so there is no x - intercept (because y can never be 0). So it does not have an x - intercept.
For slope: The line \( y=\frac{1}{2}\) is a horizontal line. The slope of a horizontal line is 0.

Answer:

The line \( x + 2 = 0 \) has x - intercept \(\boldsymbol{-2}\). It \(\boldsymbol{does\ not}\) have a y - intercept. The slope of this line is \(\boldsymbol{undefined}\). The line \( 4y = 2 \) has y - intercept \(\boldsymbol{\frac{1}{2}}\). It \(\boldsymbol{does\ not}\) have an x - intercept. The slope of this line is \(\boldsymbol{0}\).