Graphs

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Straight Line Graphs 1

Straight lines are the simplest functions to represent on a graph, as they involve equations where the highest power of x is 1.

We can plot a straight line graph by finding two points and drawing the line through them.

The equation of a line helps us find values for the $x$ and $y$ coordinates.

Let's draw the line for $y=2x+3$ .

The easiest point to find is when $x=0$ so what is the $y$ coordinate when $x=0$ ?

The first point we have found is $(0,3)$ .

This is plotted on the graph here.

Let's plot a second point for the line $y=2x+3$ . What is the $y$ coordinate for this point when $x=-1$ ?

The second point we have found is $(-1,1)$ .

This is plotted on the same graph as $(0,3)$ .

Now we join the two points and extend the line either side of them.

We have drawn the line with equation $y=2x+3$

The simplest line equations are vertical or horizontal lines.

Let's look at vertical lines first.

We seen that a vertical line has an equation of the form $x=a$ . This line is horizontal, what do you think the equation of this line is?

An important point on a straight line graph is the $y$ intercept.

This is where the line crosses the $y$ axis. When writing the $y$ intercept we only write the $y$ coordinate.

Looking at the graph, what is the $y$ intercept for this straight line?

What is the $x$ coordinate at the $y$ intercept?

What is the $y$ intercept on the graph of $y=3x-5$ shown here?

This is the graph of $y=-0.25x+2$ . What is the $y$ intercept of this straight line graph?

Summary! To plot a straight line graph, we need two points.

We can find more points, but we only need two.

This is the line with equation $y=-2x+4$ .

We can find two point - first when $x=0$ we find that $y=-2\times 0+4=4$ , when $x=2$ we find that $y=-2\times 2+4=0$ and the two points we need are $(0,4)$ and $(2,0)$ .

A vertical line always has the equation $x=a$ where $a$ is any number.

This is the graph of $x=6$ .

A vertical line always has the equation $y=a$ where $a$ is any number.

This is the graph of $y=-3$ .

The $y$ intercept is the $y$ coordinate where the graph crosses the $y$ axis, that is when $x=0$ .

Here the $y$ intercept is $4$ .