Question

y = x - 4
option 1
option 2

Explanation:

Step1: Analyze the equation \( y = x - 4 \)

The equation is in slope - intercept form \( y=mx + b \), where the slope \( m = 1 \) (positive, so the line should be increasing from left to right) and the y - intercept \( b=-4 \) (the line crosses the y - axis at \( (0,-4) \)).

Step2: Analyze each option

• Option 1: The line has a positive slope (increasing from left to right) and when \( x = 0 \), we can check the y - value. Let's substitute \( x = 0 \) into \( y=x - 4 \), we get \( y=-4 \). The line in Option 1 seems to have a y - intercept around \( - 4 \) and a positive slope, which matches \( y=x - 4 \).
• Option 2: The line has a negative slope (decreasing from left to right), which does not match the slope of \( y=x - 4 \) (slope = 1, positive).
• The third option (the horizontal line) has a slope of 0, which does not match the slope of 1 for \( y=x - 4 \).
• The fourth option: When \( x = 0 \), the y - intercept is not \( - 4 \), so it does not match \( y=x - 4 \).

Answer:

Option 1