Final answer:
To model the price of a cab car, we can use the equation y = 2x + 1, where y represents the price and x represents the number of miles. The slope is 2, indicating that the price increases by $2 for each additional mile. The y-intercept is 1, representing the initial cost of the cab ride.
Step-by-step explanation:
To find a linear equation that models the price of a cab car, we need to identify the slope and the y-intercept. Let's assume the price of a two-mile cab ride is $5, and the price of a six-mile cab ride is $13.
We can use the slope-intercept form of a linear equation, which is y = mx + b. In this equation, y represents the price of a cab ride and x represents the number of miles. The slope (m) represents the rate at which the price increases per mile, and the y-intercept (b) represents the initial cost.
To find the slope, we can use the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line. Using the given information, we have m = (13 - 5) / (6 - 2) = 2. The slope is 2.
To find the y-intercept, we can substitute one of the points (2, 5) into the equation and solve for b. Plugging in the values, we have 5 = 2(2) + b. Solving for b, we get b = 1. Therefore, the y-intercept is 1.
Putting it all together, the linear equation that models the price of a cab car is y = 2x + 1. The slope is 2, and the y-intercept is 1.