I will have to do some more research on this subject, as a fraction the 8/3 = 2
.................................................. .................................................. ...2/3

as a decimal this equates to 2.66 recurring.

My coordinates of (5,3)(-7,7) don't reflect the answer found?

Another way of doing this: Any (non-vertical) line can be written in the form y= ax+ b. Setting x= 5, y= 3, we have the equation 3= 5a+ b. Setting x= -7, y= 7, we have the equation 7= -7a+ b. Subtracting the second equation from the first eliminates b: 3- 7= 5a- (-7a). -4= (5+ 7)a, -4= 12a, a= -4/12= -1/3 (which is an exact answer where "a= -.33" is only approximate).

Now, my question is, why do you say "even I know that the gradient of that graph is more than -0.33"? The line runs from (-7, 7) to the right down to (5, 3). With a "run" of 12 there has been a "rise' of -4. The line goes down 1/3 the distance it goes to the right. That surely looks like "-1/3" to me!

What method have you learned for finding a straight line?

I prefer the one which says where is a given coordinate and is the gradient.

To find the gradient use the equation where are two points on the line. As long as you are consistent with which point is 1 and which is 2 the order does not affect the answer which you found out in the OP.

In this question we have the points (5,3) and (-7,7). Using the equation above [(-7,7) is (x_1,y_1) here] we work out the gradient .

Spoiler:

It doesn't matter because if we look at what happens when we multiply top and bottom by -1 (which we know doesn't change the value):

You don't need to know why it is so for this example, but as long as you're consistent you'll get the correct gradient

Now we know that we can sub it in to the equation of a line using either of our coordinates. I shall choose (5,3) as it contains no negative numbers

and upon adding three to both sides:

it is up to you to arrange that into the form

edit: perhaps Wolfram will be of use as a visual aid

btw: if you don't use latex can you just use plain text with brackets please? Your working is almost impossible to read. (y2-y1)/(x2-x1) = m is much easier!

What method have you learned for finding a straight line?

I prefer the one which says where is a given coordinate and is the gradient.

To find the gradient use the equation where are two points on the line. As long as you are consistent with which point is 1 and which is 2 the order does not affect the answer which you found out in the OP.

In this question we have the points (5,3) and (-7,7). Using the equation above [(-7,7) is (x_1,y_1) here] we work out the gradient .

Spoiler:

It doesn't matter because if we look at what happens when we multiply top and bottom by -1 (which we know doesn't change the value):

You don't need to know why it is so for this example, but as long as you're consistent you'll get the correct gradient

Now we know that we can sub it in to the equation of a line using either of our coordinates. I shall choose (5,3) as it contains no negative numbers

and upon adding three to both sides:

it is up to you to arrange that into the form

edit: perhaps Wolfram will be of use as a visual aid

btw: if you don't use latex can you just use plain text with brackets please? Your working is almost impossible to read. (y2-y1)/(x2-x1) = m is much easier!

Thank you for your help on this thread.

First in reply to another members thread, the reason I thought the gradient was wrong at -0.33 was because I compared that result to the graph that a produced and what looked back at me was in appearance significantly different, what I didn't think to do until it was pointed out was to use fractions, therefore;

-0.33 = -1/3

In relation to the work I did previously and the help received, which is greatly appreciated, however, the above technique I can't follow it the way it has been presented, my limited experience does not permit me now to understand what value has been chosen for x, as in my coordinates 5 was the x value?

Using y = mx + c

I tried the following.

y = - 1/3 x -7 + 16/3 = 7/3 + 16/3 = 23/3 = 7.7

This type of answer has been my problem all along, my coordinates are (5, 3) and (-7, 7)

So getting answers to 1 d.p is throwing me off and I can't see where I am getting it wrong?

So I keep asking myself am I getting something wrong or is there something wrong with the question being asked?

As you said you have y=mx+c and it appears that you're using the co-ordinate (-7,7) which is fine so if sub in x=-7 and y=7 then you find c.

Thus your equation is . You can test this by plugging in your other coordinate and seeing if the LHS=RHS

Thank you, it is a clear lack of understanding on my part.

I knew how to calculate the gradient, but was confused with the result obtained, that was throwing me out first.

Once that problem was solved I then hit the next hurdle which I thought I understood, but obviously not?

I then started to get confused with the fractions because I had tried to find the solution in so many different ways I completely confused myself.

In the workbook using y = mx + c, I failed to notice that "x" disapeared when the example was being worked out, therefore when I was trying to work out a solution I was including a value for "x", which was giving me incorrect results.

This was part of the confusion in the book;

y = mx + c

gradient = 3/2

y = 3/2(x) + c

y = 3/2 x 1 + c

Look at the co-ordinates they used in the example (1,2)

So I started to use the same idea, however they did not include the (x 1)?