Linear equation?!?

Question

I dont understad this problem:

Directions: Write a linear equation to model each table of values. For each equation, state what the slope represents.

Question:


Hours --- Parking Fee ($)
3 --- 6.50
7 --- 12.50


I really need help! Thank you in advance! :]

Answer 1

it's like two points on a line. (3,6.5) and (7,12.5)

a slope is the difference in y, over the difference in x. such as

m = (y1 - y2) / (x1 - x2)

m = (12.5 - 6.5) / (7 - 3)

m = 6 / 4
m = 3/2

right? :)

since i used fees in y and hours in x, the slope represents $ per hour.

Answer 2

a linear equation is in the form y = mx + b

if we let hours = x and fee = y

then plug in the two points (3, 6.50) and (7, 12.50) we get two equations with 2 unknowns

6.50 = m * 3 + b
12.50 = m * 7 + b

there are a number of ways to solve this. here's the first way most people are taught.

take the first equation and solve for either m or b. I'm choosing solving for b

6.50 = m * 3 + b
b = 6.50 - 3m

next plug that value for "b" into the second equation...

12.50 = m * 7 + b
12.50 = 7m + (6.50 - 3m)
6 = 4m
m = 6/4 = 3/2

now we know m (ie the slope) for the line

y = mx+b = 3/2x + b

since we know y = 3/2 x + b if we plug back in that first data point, we can solve for b

6.50 = 3/2 * 3 + b
6.50 = 9/2 + b
6.50 = 4.50 + b
2 = b

now you know m and b for the equation y = mx+b

pluggin them in gives...

y = 3/2 x + 2

slope = 3/2, intercept = 2

Answer 3

Start with the general eq of a line (since this is linear)

y = mx + b

m is the slope and yu caculate it by finding the change in hrs divided by change in price.

change in hrs = 7-3 = 4 hrs
change in price = 12.50 - 6.50 = 6

m = 6/4 = 3/2

y = 6/4x + b
substatute 3 for x and 6.50 for y and solve for b
6.5 = 3(6/4) + b
b = 2
your equation is:

y = 6x/4 + 2

m is a slope in math, but in real life it is the rate at which you are charged i.e it is $ per hour for parking, here your rate is 3 dollars for every 2 hours or $1.50 per hour to park.