1. ## linear relations

i have no idea how to get the answers

1. do the points P(1,-3), Q(2,1) and R(2.5,3) lie on the same straight line.

2, An electronic bankteller registered $775 after it had counted 120 notes and$975 after it had counted 160 notes.
a) find the formula for the sum registered ($C) in terms of the numbe rof notes (n) counted 3. Da=10t+20 Db=20t+5, where t is the time in hours after 1.00pm a) find the time in hours at which the two cyclists are at thesame distance from the town hall step attempt. 10t+20=20t+5 -10t=-15 t=15/10 ? but the answer is 2.00pm thanks alot 2. Originally Posted by fresh_ 1. do the points P(1,-3), Q(2,1) and R(2.5,3) lie on the same straight line. The three co-ordinates are $(1, -2)$, $(2,1)$ and $(2.5, 3)$. You can find the equation of the straight line using two of these co-ordinates and testing with the final co-ordinate to see if they all lie on the same line. $m = \frac{y_1-y_2}{x_1 - x_2} = \frac{1-(-3)}{2-1} = \frac41 = 4$ $y-y_1 = m (x - x_1) \implies y-1 = 4(x-2) \implies y = 4x-7$ We have used the co-ordinates $(1, -2)$ and $(2,1)$ to calculate the gradient and the equation of the straight line so we check whether the other co-ordinate, $(2.5, 3)$, fits the line. When $x=2.5 \implies y=3$ $y = 4x-7 \implies y = 4(2.5)-7 = 3$ Therefore the three co-ordinates are $(1, -2)$, $(2,1)$ and $(2.5, 3)$ all lie on the straight line with the equation, $y = 4x-7$. 3. Originally Posted by fresh_ 2, An electronic bankteller registered$775 after it had counted 120 notes and $975 after it had counted 160 notes. a) find the formula for the sum registered ($C) in terms of the numbe rof notes (n) counted
Conduct the method in the same manner. Treat $(x, y)$ as $(n,c)$.

Therefore, the two co-ordinates are: $(120, 775)$ and $(160, 975)$.

$m = \frac{y_1-y_2}{x_1 - x_2} \implies \frac{c_1-c_2}{n_1 - n_2} = \frac{975-775}{160-120} = \frac{200}{40}= 5$

$y-y_1 = m (x - x_1) \implies c-c_1 = m (n - n_1) \therefore c-775 = 5(n-120) \therefore c=5n+175$

4. Originally Posted by fresh_
3.
Da=10t+20
Db=20t+5, where t is the time in hours after 1.00pm
a) find the time in hours at which the two cyclists are at thesame distance from the town hall step
attempt.
10t+20=20t+5
-10t=-15

t=15/10 ? but the answer is 2.00pm
Is this the full question? [ie. Is it exactly worded like the manner you have written it in?].

If so, I would also have done it in the same method as you did and obtained $t=1.5$ hours. (I'm assuming $D_a$ and $D_b$ are distance from townhall step at time $t$?)

At $t=1.5$ hours:
$D_a = 10(1.5) + 20 = 35m$
$D_b = 20(1.5) + 5 = 35m$ From town hall step.

This happens at 2.30pm.

5. Originally Posted by Air
Is this the full question? [ie. Is it exactly worded like the manner you hve written it in?].

If so, I would also have done it in the same method as you did and obtained $t=1.5$ hours. (I'm assuming $D_a$ and $D_b$ are distance from townhall step at time $t$?)

At $t=1.5$ hours:
$D_a = 10(1.5) + 20 = 35m$
$D_b = 20(1.5) + 5 = 35m$ From town hall step.

This happens at 2.30pm.
here is the complete question. i thought it wasn't necessarily to type up all of it
but here it is
the distances, Da km and Dbkm, of cyclists A and B traveling along a straight road from town hall step are given respectively by.
Da=10t+20
Db=20t+5, where t is the time in hours after 1.00pm
a-find the time in hours at which the two cyclists are at the same distance from the town hall step

there , and thanks for the help on the other questions

6. Originally Posted by fresh_

1. do the points P(1,-3), Q(2,1) and R(2.5,3) lie on the same straight line.
Here is another way to do this problem.
Show $m_{PQ} = m_{QR}$ where $m_{PQ}$ is slope of $PQ$ and $m_{QR}$ is slope of $QR$.

7. For the first question, here's another way

Use the area formula and see if the value is 0, if it is 0 then they are collinear if not , then they aren't and hence form a triangle.

The area formula :- x1(y2-y3)+x2(y3-y1)+x3(y1-y2)

where x1 depicts first x coordinate and so on and y1 depicts first y coordinate and so on..

8. help with the 3rd one

the distances, Da km and Dbkm, of cyclists A and B traveling along a straight road from town hall step are given respectively by.
Da=10t+20
Db=20t+5, where t is the time in hours after 1.00pm
a-find the time in hours at which the two cyclists are at the same distance from the town hall step