Question

i need help with the file i add
pl look at it help me
I WILL AWARD MEDAL!!!!

Answer 1

i need help with the file i add
pl look at it help me
I WILL AWARD MEDAL!!!!

Answer 2

This is about linear graphs, right?

Answer 3

Since we are told to use the first and the last point on the graph to determine a line that models the data, we need to find the gradient (steepness) of the line that join the first and the last points.

Answer 4

To find the gradient of the line joining the first and the last point, we need to divide the difference in y co-ordinate by the difference in x co-ordinate.
Gradient : \[\frac{ \Delta y }{ \Delta x }\]
which is
\[\frac{ y1 - y2 }{ x1-x2 }\]
where y1 and x1 are the co-ordinates of the last point and y2 and x2 are the co-ordinates of the first point. Substituting the values will give us
\[\frac{ 207-177 }{ 2005-1999 }\]
which equals to 5. This mean the gradient of the line joining the first and the last point is 5.
Now that we know the gradient, we can use the formula
\[y-y1 = m(x-x1) \] to get the equation of the line. (Note that y1 and x1 have to be the co-ordinates of the same point)
We can use the co-ordinates of either the first point or the last point. It doesn't matter. For this question I am going to use the last point.
For the last point:
x1 = 2005
y1 = 207
m = 5
hence

\[y-207=5(x-2005)\]\[y-207=5x-10025\]\[y=5x-9818\] Therefore the equation of the line joining the first and the last point is\[y=5x-9818\]
You can check the answer by substituting a value of x and seeing whether you get the corresponding y-value.