HW Linear equation?

Question

Please explain how to do this. Give lots of details

A 3-mile cab ride costs $3.00. A 6-Mile cab ride costs $4.80. Find a linear equation that models cost (c) as a function of distance (d).

Answer 1

Hi, a linear equation is one that expresses a line. You have 2 pairs of values here, these correspond to two points on the coordinate system. Think of the x-axis as being distance and the y-axis as being cost. Thus, the coordinates you have are:

(3, 3.00) and (6, 4.80)

To find an equation, all you have to do is find the line passing through these points. You can do this in a number of ways and I'll show you one now.

The equation of a line is y = mx + b. In our model this is the same as c = md + b, where c is the cost and d is the distance. The slope is the change in cost per unit distance:

(4.8 - 3)/(6 - 3) = 1.8/3 = 0.6 dollars/miles

Thus we have,

c = 0.6d + b

Given the slope, we can use either of the points to find "b" the y-intercept. This is because an equation describes every point on the line. Using the first point:

3.00 = 0.6 * 3 + b
so b = 3 - 1.8 = 1.2

So the final equation is:

c = 0.6*d + 1.2
where c is in dollars and d is in miles.

Answer 2

A cab ride has an initial cost of flag fall and a per-mile charge. So the equation is f + d*m = t, where f = flag fall, d is distance, m is per-mile charge, and t is total.

Using your data (and working in cents rather than dollars to avoid decimals):

f + 3*m = 300

and

f + 6*m = 480

Subtract first from second:
3*m = 180
so m = 60. Plug this in to first:

f + 3*60 = 300
f = 120.

Now check to make sure there were no careless errors:

120 + 60*3 = 300 ... check
120 + 60*6 = 480 ... check

So the equation is as above (putting back the decimal point and using your variables):

1.20 + .60*d = c


Add T of course for the tip.

Answer 3

Linear equations are functions of two variables, usually x and y.
Taking the form y = mx + b
Let y = the fare and x = the distance. Now, we see that the fare is really just a line on the x-y plane. So first we must find the slope.

(4.8-3)/(6-3) = 1.8/3 = .6 = m (slope)

Now plug in a set of points for x and y to find b. You can check by plugging in the other set to be sure you have the right equation.

Answer 4

hey, ok
so let x be the cost in $ per mile, d me distance...in miles.... let r be the crafty charge that the cabbie always sticks on at the end of the journey. Because the question says that you're looking for a linear equation you know that it'll be of the form

c=xd+r

so you have 3x+r =3
also 6x+r=4.8

these are simultaneous equations, subtract the first one from the second like this;

(6x+r) - (3x+r) = 4.8 - 3
ie 3x=1.8, x=0.6

you subtracted the equations to get rid of the r term, dont worry itll be back (damn cabbies)

so x=0.6, but from the first equation you know that 3x+r=3
ie that r=3-3x = 3 - 3x0.6 = 3 - 1.8 = 1.2

hey presto, your linear equation is c = 0.6d + 1.2

Answer 5

It's just like using two points to find the equation of a line.
Instead of (x,y) you have (d,c) with the two points being
(3, 3.00) and (6, 4.80). I'll let you do the datails.

Answer 6

we have 2 eq y=3/5x-3 y=2x+4 Since a=b c=b then a=c so 3/5x-3=2x+4 7/5x=-7 x=5*(-7)/7 x=-5 then we substitute x=-5 in y=2x+4 y=2(-5)+4 y=-6

Answer 7

c: cost
d: distance
x: a constant added or subtracted to the function.
cpm: cost per mile

c= (cpm * d)+x

solve both equations
3=(cpm*3) + x ........ (1)
4.8=(cpm*6) +x........(2)

(2) - (1)
1.8=3cpm
cpm = 0.6

substitute into (1)
3=(0.6*3) + x
x = 1.2

confirm into (2)
4.8 = (0.6*6) + 1.2

finally
c=0.6d + 1.2

Answer 8

I believe you need more than two values to make an equation. Try using a TI calculator.

Answer 9

c=3+(d-3)*0.60

Answer 10

$3.00+(d-3)*$0.60