I am given;
y = 1/2x + 3
I am asked to produce a table of data. I have no problem working this out, however I can't see where the value 1/2 originates from?
So if I am asked in a different question to work out the equation of the line, and given (-4. -2) and (2, 7) I can put the table together, but y = ? to multiply the values.
How do I work this out ?
I have worked out how to find all the corresponding values of y, but I don't know how to work out the value of y before I start multiplying out the y multiplied by x values = new y values?
I am still learning, please advise if what I think I have learned here is right so far.
In my maths question I am asked to find the equation of the line, the information I have been given is;
(-4, -2) and (2, 7)
I have worked out that I am supposed to work out the gradient of the line after plotting the graph, thw gradient I have found to be - 1.71.
Using this I have worked out that;
y = -1.71 times (x) + 2
using the above I can then find my new values of y;
y = -1.71 x -4 = 8.84 etc
so the equation of the line would be;
y - -1.71x + 2
Please advise if I have worked out the equation of the line correctly and used the right techniques
You appear to have many misunderstandings. If you show how you calculated your value for m, some of them can can be pointed out.
Reviewing your class notes and textbook might help. But from what I have seen I think you will need to see your instructor for extensive one-on-one help.
Any (non-vertical) line in a coordinate system can be written y= ax+ b. Given that the line goes through the two points (-4, -2) and (2, 7) you can put those (x,y) values in the equation to get -2= -4a+ b and 7= 2a+ b which are easy to solve for a and b.
Keeping it as simple as possible, I have (-4, -2) and (2, 7). therefore;
x = -4 when y = -2, and
x = 2 when y = 7.
Draw this graph and when x = -4 and y = -2, the slope of the line will CUT the x axis at about -2.6, and when x = 2 and y = 7, the slope of the line will CUT the y axis at y = 4.
I worked out the gradient of the line, RISE over RUN = 1.54
My table of data
x = -4, -3, -2, -1, 0, 1, 2
y = -4.16, -2.62, -1.08, 0.46, 0, 3.54, 5.08
I found that y = -4.16 and x = -4
-4.16 / -4 = 1.04
y = 1.04 + 2
gradient = 3
surely I can't be that far out?
In my example the book says; the x intercept is the point where the line crosses the x axis, and the y intercept is the point where the value of y crosses the y axis, so reading from my graph;
y = 0 then x = -2.6, and when x = 0 then y = 4
we don't seem to have any other information, and this does'nt sem to answer the original question?
so the gradient of the line seems to be 1.5, and the equation of the line seems to be;
y = 1.5x + 2
Have I got this right?
We have the gradient, so we know that y=1.5 + c
We need to find c. This can be done using one of our pairs of values, in the above equation. i'll use x=2, y=7
7 = 1.5*2 + c
7 = 3 + c
c = 4
So the solution is y=1.5x + 4
I dont see where you got 2 from. It doesn't appear anywhere else in your post. You have correctly identified the y intercept at x=0,y=4.
i used one of the points we were given: x=2, y=7.
The equation for the line is: y = 1.5x + c
where c is an unknown number to work out.
substitute in a pair of values we know: x=2, y=7.
7 = 1.5 * 2 + c
7 = 3 + c
Solve that equation in the normal way
7 - 3 = 0 + c
4 = c
Return to the original equation:
y = 1.5x + c
y = 1.5x + 4
This is not the only way of finding the answer. you may have been taught a different one.