Graphs

Ok, so admittedly on this one I cheated, I drew the graph on a computer. But as always it's harder than it seems to draw by hand. They have selected weird points, so we have to first work out our spacing on the y axis. Then you will get points for;

• x on the horizontal axis, and y on the vertical axis
• equal spacing on both axes
• appropriate spacing to clearly show the points
• line of best fit drawn through points
• EVERYTHING WITH A RULER!!!

We first need to draw a graph for this problem. This is easier than it sounds, as there are usually a lot of things we overlook. Be sure to include

• The x axis MUST be horizontal, and the y axis vertical.
• equal spacing on both the x axis and y axis.
• Choose appropriate spacing on each axis.

Use a ruler and square paper!
The second part of this question asks for the equation describing the data. We will use the equation y=mx+c  to solve this.

First, we will find the m value, using the points (0, 2) and (1, 5).

Then we can find the y intercept. In this graph it's easy, the c value is where the line cuts the y axis, in this case at 2.

There are 2 different ways to calculate the answer here. We can use the graph which is very easy, or we can use the equation, which may be more accurate. Here we will use the graph. First find the x value (input) then follow with a straight line up to the line, and then across to the y axis. This will be your answer:

We need to make a neat graph, you will get points for

• y-axis vertical, x-axis horizontal
• equal spacing on the x and y axis
• clear points marked
• a smooth hand-drawn line for the parabola

Not much to this one, when they say "law" they mean the equation of a line, as we are talking about a straight line, there isn't much more to it that just y=mx+c

We can use the graph to find an estimate for the value of x when y=5. We just need to draw a horizontal line at y=5. Then we can see where it touches the curve, and trace these points down to the x-axis, this gives us our two solutions, both are valid.

Let's calculate the "m" value using the m equation shown below. This can also be done using rise over run. we can see for every one step we take in the x direction we take 0.3333 of a step in the y direction.

The "c" is the y-intercept, this can clearly be seen both in the table and on the graph, where c =-1

Then we just put it all together:

For this question, we need to plug in values of x into the equation and calculate a value for y. we can show this all in a neat table. I included a screenshot of my calculator just to show you how to enter it all in, you can backspace and reuse the same equation so you don't have to retype the whole thing each time!