Question

a cyclist travels along a direct route from town a to town b.
x = the distance of the cyclist from town a in miles.
y = the distance of the cyclist from town b in miles.

Explanation:

To solve this, we analyze the relationship between \( x \) (distance from A) and \( y \) (distance from B). The total distance between A and B is constant, so \( x + y = \text{constant} \) (let's call it \( D \)). Rearranging gives \( y = D - x \), which is a linear equation with a slope of \( -1 \) (since \( y = -x + D \), in the form \( y = mx + b \) where \( m = -1 \) and \( b = D \)).

Step 1: Analyze the equation form

The equation \( y = -x + D \) represents a straight line with a negative slope (because the coefficient of \( x \) is \( -1 \)).

Step 2: Match with the graphs

• Graph A: Curved, not linear. Eliminate.
• Graph B: Straight line with negative slope (decreasing as \( x \) increases), matching \( y = -x + D \).
• Graph C: Straight line with positive slope (increasing as \( x \) increases), which would imply \( y = kx \) (no constant term), not matching \( x + y = D \). Eliminate.
• Graph D: Straight line with positive slope, starting at \( (0,0) \), which also doesn’t match \( y = D - x \) (when \( x = 0 \), \( y = D \), not \( 0 \)). Eliminate.

Answer:

B (the graph with a straight line decreasing from the y - intercept as x increases)