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A 7 mile cab ride cost $6.80. A 9 mile cab ride cost $8.40 find a linear equation that models, a relationship between cost and distance

User RussS
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2 Answers

4 votes

Answer:

m = ($8.40 - $6.80)/(9 - 7) = $1.60/2

= $.80/mile

$6.80 = ($.80)(7) + b

$6.80 = $5.60 + b

b = $1.20

y = .80x + 1.20

User Aneh Thakur
by
8.5k points
1 vote

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.

User Igor Lankin
by
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