In this chapter we’re going to be looking at y=mx+c graphs. We shall explore the effects of m and c on the line in the y=mx+c equation. We shall then explore how to find the equation of a line drawn on a graph paper.
Plot the graph of y=2x+1 To plot a graph we usually draw a table and then try to find the value of y for the chosen x values. You need to editing and make sure that the chosen values are close to each other, for example 1 to 10. Below is the table that will help us plot the graph of y=2x+1.
x y 0 1 1 3 2 5 3 7 4 9
Now we can plot these values on the graph as shown below. Now we join the plotted points with a single straight line.
M and C in y=mx+c In the equation y=mx+c m changes the steepness of the line. The following shows a graph which has lines whose m values have been changed.
The C in y=mx+c changes where the line intercepts the y-axis by moving it down or upwards. The following graph has lines whose C are different.
Above we’ve seen that as the m value changes the steepness of the line changes. The steepness of the line in mathematics is known as gradient
We find the gradient on a straight line by dividing the number of units covered by a line across with the number of units covered by the line down. The following is the line of y=½x+c
One divided by two gives ½, this is what is known as the gradient of the line.
Finding the equation of a straight line Below we can see a graph whose equation is unknown.
Since the above is a straight line. The equation will be in the form of y=mx+c. We need to find the values of m and c in the equation. We know that the c value indicates where the line intercepts the y-axis so;
We know that m is the gradient of the line and we find this by dividing the upwards coverage with the downwards coverage;