Question

graphing lines
match the graph of each line:
1)

1. y = 4
2. x = 4

2)
4)

1. y = 2x + 4

Explanation:

Step1: Analyze \( y = 4 \)

The equation \( y = 4 \) represents a horizontal line where the \( y \)-coordinate is always 4, regardless of the \( x \)-value. So we look for a graph that is horizontal and passes through \( y = 4 \).

Step2: Analyze \( x = 4 \)

The equation \( x = 4 \) represents a vertical line where the \( x \)-coordinate is always 4, regardless of the \( y \)-value. So we look for a graph that is vertical and passes through \( x = 4 \).

Step3: Analyze \( y = -\frac{1}{2}x \)

This is a linear equation in slope - intercept form \( y=mx + b \) with \( m=-\frac{1}{2} \) (slope) and \( b = 0 \) (y - intercept). The slope is negative, so the line should decrease from left to right and pass through the origin \((0,0)\).

Step4: Analyze \( y=2x + 4\)

This is a linear equation in slope - intercept form with \( m = 2 \) (positive slope, so the line increases from left to right) and \( b=4 \) (y - intercept at \((0,4)\)).

For \( y = 4 \): We look for the horizontal line at \( y = 4 \).
For \( x = 4 \): We look for the vertical line at \( x = 4 \).
For \( y=-\frac{1}{2}x\): We look for the line with negative slope passing through the origin.
For \( y = 2x+4\): We look for the line with positive slope and y - intercept at \( (0,4) \).

Answer:

• For \( y = 4 \): The horizontal line graph at \( y = 4 \).
• For \( x = 4 \): The vertical line graph at \( x = 4 \).
• For \( y=-\frac{1}{2}x\): The line with negative slope through the origin.
• For \( y = 2x + 4\): The line with positive slope and \( y \)-intercept at \( (0,4) \).

(Note: Since the graphs are a bit unclear, but based on the equations, we can match them as per the properties of linear graphs. If we assume the small graphs on the right:

• \( y = 4 \) matches the horizontal line graph (probably the one with horizontal lines and \( y = 4 \) marked).
• \( x = 4 \) matches the vertical line graph (probably the one with vertical lines and \( x = 4 \) marked).
• \( y=-\frac{1}{2}x\) matches the line with negative slope through the origin (the one going from the second quadrant to the fourth quadrant through (0,0)).
• \( y = 2x + 4\) matches the line with positive slope and \( y \)-intercept at (0,4) (the one going from the third quadrant to the first quadrant with \( y \)-intercept at (0,4)) )