Final answer:
To find a linear equation representing cab fare as a function of distance, calculate the slope using two given fare-distance points and then use one point to determine the y-intercept, resulting in C = 0.80D + 1.20.
Step-by-step explanation:
The task is to find a linear equation that models the relationship between cost and distance for cab rides. We have two points to consider: (1, $6.80) for a 7-mile ride and (2, $8.40) for a 9-mile ride. To find a linear equation in the form of y = mx + b, where m is the slope and b is the y-intercept, we first calculate the slope using slope formula, "m = (y2 - y1) / (x2 - x1)". In this case, "m = ($8.40 - $6.80) / (9 - 7) = $1.60 / 2 = $0.80 per mile". This is our slope.
Next, we can find the y-intercept b by plugging one of the points and the slope into the linear equation. Let's use the first point (7 miles, $6.80) and the slope $0.80: $6.80 = $0.80(7) + b. Solving for b gives us $6.80 = $5.60 + b, so b = $6.80 - $5.60 = $1.20. Our y-intercept is $1.20.
So the linear equation modelling the cost C in dollars of a cab ride for a distance D in miles is C = 0.80D + 1.20.