Question

Write the equation for this situation: the cost, c, in dollars of a car rental is equal to 10 dollars plus 1/2 the miles driven, m.

Then graph the equation and use the graph to determine the cost of the car rental if the number of miles driven is 12. Please show all of your work. Submit your graph through the dropbox

Answer 1

Ok so let's get it started =). The problem tells you the the cost, c, is equal to..... So we know the first part of the equation is "c", the rest of the equation should tell us how to calculate c

So
1. C = ?
2. The second part of the problem tells you that there is a static cost of 10 dollars. So you can represent that with "10". So now we have c= 10 + ?

Answer 2

3. The problem finally tells you that there's an additional cost - 1/2 dollars per every mile driven ("m"). So that means 1/2m is the cost per mile.

Answer 3

putting it all together:
4. c = 1/2m + 10

Answer 4

c = 10 + .5m

if the miles (m) = 12, then just subsitute that into the equation:

c = 10 + (.5)(12)
c = 10 + 6
c = $16

Answer 5

that *should* look like a slope intercept equation to you (y=mx+b) - with m=1/2 and "b" = 10

Answer 6

The easiest way (for me) to get started with word problems is to just dive right in, filling in the variables that you can understand from the word problem. So in this case you knew that "c" was the left hand side from the way it was worded (equal to....this other stuff). And then we just started translating the "other stuff" into a math equation

Answer 7

or rather, expression

Answer 8

ok but we still have 12 miles

Answer 9

Yes, so the question is asking you to graph a slope/intercept equation, and then use the "x" value of 12 as one of your data points. That is, c = 1/2m + 10 is like graphing y = 1/2x + 10 - the only difference is what you call the variables. (c and m vs. x and y)

Answer 10

i have to put this on a graph when i finish

Answer 11

so
x = 1, y = 1/2*1 + 10
x = 2, y = 1/2*2 + 10
x = 3, y = 1/2*3 + 10...
x = 12, y = 1/2*12 +10 = 16

Answer 12

ok i getting what you saying i get confused about graphing

Answer 13

The simple way to graph a slope intercept equation is to use the slope itself. You know there is a point at (0,intercept) - in this case, at (0,10). Then since you know the slope is "1/2" , you know that for every number you move to the right (increase the x value), the y value increases by 1/2. That's the definition of a slope.

So intuitively, you know there are points at (0,10), (1,10.5), ( 2,11), (3,11.5) - it should and at (12,16)

Answer 14

pretend the equation that you generated looks like y=1/2x + 10 instead of c=1/2m + 10. They are the same equations, different variables, but the same shape of graph. In this case, the "y-axis" is called "c" for cost, and the x axis is called "m" for miles driven.

Answer 15

But graphing it the same thing, the the axis *can* be labeled differently if you choose - it's just using different variable names.

Answer 16

If you're asking how to graph a slope intercept equation (y=mx+b) , just choose two values of x, plot them, and then use a ruler to draw a straight line through those two points. You can do this because a slope-intercept equation is always a straight line.

Answer 17

then to find the value for "12", just look on the line that you drew for what the y value is when x is 12. It should be 16 =)

Answer 18

so plot one point at (0,10) (y=0*1/2 + 10 = 10), one point at (2,11) (y=2*1/2 + 10 = 11), and then draw a straight line through them

Answer 19

so i should write the equation out like this x=1,y=1/2*1+10
x=2,y=1/2*2+10,x=3,y=1/2*3+10,x=12,y=1/2*12+10=16

Answer 20

Three parts really.
1. The direct translation of the word problem is c=1/2m +10
2. This is exactly like a slope intercept equation - y=mx+b. So choose two points to plot on a graph (two values of "x", usually one is the intercept where x=0). And then using those two points, draw a straight line through them.
3. On that graph, look at the y value where x =12 (what y value is the line that you drew when x = 12). Circle that point, and note that it's "16".