## Thursday, 3 July 2014

### Homework: Study Notes (p30) Discussion 1

How would you determine if the points A (2, -5) and B (5, 2) lie on the straight line y = 3x - 5?

Key in your responses in "Comments".
Remember to enter your group number.

#### 17 comments:

1. This comment has been removed by the author.

2. A is obviously not on the line. -5 is the y intercept, thus if A is on the line, the coordinates would be (0, -5)

To find out if B is on the line, substitute -5 as c. Then substitute x and y with the coordinates in B. If x and y is on the line, c=5 would be found.

Grp 3

3. We can substitute the y and x in y=3x-5 with the x and y points in A and B. So these are the workings:

A:
y=3x-5
-5=(3x2)-5
-5=6-5
-5=1
Since -5 does not equal to 1, then point A is definitely not on the straight line.

B:
y=3x-5
2=(5x3)-5
2=15-5
2=10
Since 2 does not equal to 10, then B is not on the line.

Group 1

4. If A and B both lie on the straight line, all we need to do is to calculate the gradient using (2, -5) and (5, 2) to see if the result agrees with the equation.

m = (-5-2)/(2-5)
= 7/3

The calculated gradient with the 2 points A and B is 7/3. But, the equation states that the gradient is 3, so the 2 points are not on the line.

5. To find out is A and B is on the line, we can just substitute in the coordinates into the equation.

For Point A, the coordinates are (2,-5)
So the equation is y=3x-5,
therefore the equation will become:
-5=3(2)-5
-5=6-5
-5≠1
We can easily conclude that A does not lie on the graph.

For B, we can also use the same method. B's coordinates are (5, -2)
So the equation will become
-2=3(5)-5
-2=15-5
-2≠10

Again, we also can easily conclude that B is also not on the line.

Group 4

6. How would you determine if the points A (2, -5) and B (5, 2) lie on the straight line y = 3x - 5?

We can substitute the coordinates into the equation. In A, we can the substituted equation is -5=3(2)-5. The equation obviously does not match. Both sides of the equation are unequal. Thus, A is not the point on the line.

Next, for B, the equation will be 2=3(5)-5 which is 2=10. The equation is invalid once again, and we can conclude that B is not a point on the graph.

Group 2

7. we can subsitute the actual numbers to the equations
it would look like "-5 = 6 - 5" and this is obviously wrong, hence A does not lie on the line

for B it will look like "2 = 15 - 5" which is once again wrong since it does not add up, hence B does not lie on the line

group 1

8. In order to solve this, we just need to substitute the points into the equation… If the points satisfy the equation, the the points do sit on the straight line, y=3x-5.

So here is my attempt to solve this question:

For ordered pair (2,-5),

y=3(2)-5
=6-5
=-1,
Therefore, since (y) is (-1) and not (-5), this ordered pair does not satisfy the equation y=3x-5 and hence, this coordinate does not lie on the equation of the straight line.

For ordered pair (5,2),

y=3(5)-5
=15-5
=10,
Therefore since (y) is (10) and not (2), this ordered pair does not satisfy the equation y=3x-5 and hence, this coordinate does not lie on the equation of the straight line.

1. Oh… and also I am from Group 2.

9. We can substitute y=mx+c with y=3x-5 If both points A and B lie on the same line, we can just find the gradient of a and b: m= (-5-2)/(2-5)= 2 1/3

The calculated gradient with the 2 points A and B is 2 1/3. But the gradient stated in the question is 3 thus, point A and B are not on the straight line.

1. Group 2(forgot to mention it)

10. How would you determine if the points A (2, -5) and B (5, 2) lie on the straight line y = 3x - 5?

Using y=mx +c ,
m = gradient
= y1-y2
-------------
x1-x2

= -5 - 2
------------
2 - 5

= -7
-------------
-3
= 2.33 (3 sf)

y= mx+c
y = 2.33 x + -5

Thus , points A and B are not on the same line.

Group 4

11. A) y=mx+c
If (x,y) = (2,-5)
-5=3(2)-5
=1

Since the answer is not 0 the coordinates do not lie on the line.

B) if (x,y) = (5,2)

then 2=3(5)-5

=10

so it is also not on the line as any point that lies on the line must have a final answer of 0 after being simplified.

Group:4

12. POINT A =(2,-5)
So y=3x-5,
thus -5=3(2)-5
-5=6-5
-5≠1
SO obviously Point A is not on the Line

Point B(5, -2)
So -2=3(5)-5
-2=15-5
-2≠10

SO Point B is also not on the line

Grp 3 :D

13. Point A=(2,-5)
Substitute x & y coordinates with x & y in y=3x-5
Thus, y=3x-5
=-5=6-5
-5=1 which is wrong, so A is not on the line

Point B can also be done with this method

y=3x-5
2=15-5
2=10 which is again wrong

Both points A and B are not on the line y=3x-5

Group 1

14. This comment has been removed by the author.

15. In order for both points A and B to line on a straight line, their gradient* has to be the same as the given line. Hence, we calculate the gradient:
(2 (-5)) / (5 - 2) = 7/3

As you can see, the gradient of the given line and *[the gradient of the line made when points A and B are joined] are not the same. Thus points A and B do not lie on the line.

Group 3