In New York City, the cost to take a taxi can be represented with the equation y = .40x + 2.50, where x is the number of miles driven and y is the total cost. The cost of a taxi in San Francisco is shown in the table below.
Answers
Answer:
y = 0.45x + 2.85
Step-by-step explanation:
to solve we can first subtract the initial cost by taking the price at 0 miles and subtracting it from one of the higher numbers, we will go with $5.10 at 5 miles for this example
5.10 - 2.85 = 2.25
now we have the price for just the 5 miles separated from the initial cost, but we still need to figure out what each single mile is, so now we just divide by 5, one for each mile
2.25 / 5 = 0.45
so $0.45 is the cost to ride for one mile, and the initial cost is 2.85, now all we have to do is implement those numbers into a formula, since 0.45 is for each mile, it is multiplied by the miles, or x, so that will be put together below
0.45x
then we have the value to add to that, 2.85
0.45x + 2.85
and that is = to y, the cost to ride in a San Francisco taxi
The cost of a taxi in San Francisco is higher compared to New York and the equation of line is y = 0.75x + 2.85
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
y = 0.40x + 2.50 be equation (1)
where y represents the cost of the taxi in New York for x miles driven
Let the first point be P ( 0 , 2.85 )
Let the second point be Q ( 5 , 5.10 )
Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( 5.10 - 2.85 ) / ( 5 - 2 )
Slope m = 0.75
And , the equation of line for the cost of the taxi in San Francisco for x miles driven is given by
y - ( 2.85 ) = ( 0.75 ) ( x - 0 )
Adding 2.85 on both sides , we get
y = 0.75x + 2.85 be equation (2)
So , when x = 1 mile
y = $ 3.60
And , when x = 1 in equation (1) , we get
y = $ 2.90
Therefore , the cost of a taxi in San Francisco is higher compared to New York
Hence , the equation of line is y = 0.75x + 2.85 for the cost of taxi in San Francisco
To learn more about equation of line click :
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