## What you need to know

Things to remember:

• Co-ordinate are given by values of $x$ and $y$ and look like (x,y).
• We can substitute values of $x$ and $y$ into the straight line to see if they fit.
• If the equation is true, then the points lie on the line.
• If the equation is not true, then the point does not lie on the line.

Does the point (3,7) lie on the line $3y=5x+1$

If we look at the point and straight line plotted on the $x$ and $y$-axis we can clearly see that the point isn’t on the line

Although it is clear that the point doesn’t lie on the line, it is time consuming to draw it; luckily for us, we have a quicker method of doing this.

Let’s think about what the co-ordinate of this point is telling us. Well, co-ordinates represent values $x$ and $y$. The co-ordinate here are telling us that $x=3$ and $y=7$. Well, not that we have these values, we can actually substitute them into our equation.

$$3y=5x+1$$

$$3\times7=5\times3+1$$

$$21=15+1$$

$$21=16$$

Well, this clearly isn’t true, 21 doesn’t equal 16, so the point doesn’t lie on the line. So, to check if a point lies on a line, we just need to substitute the values into the equation.

Does the point (6,3) lie on the line $5y=3x-3$

$$5y=3x-3$$

$$5\times3=3\times6-3$$

$$15=18-3$$

$$15=15$$

This is true, 15 does equal 15, so (6,3) must lie on $5y=3x-3$.

## Example Questions

#### Question 1: Does the point (7,7) lie on the line $2y=x-9$

$$2y=x-9$$

$$2\times7=7-9$$

$$14=-2$$

This isn’t true, 14 does not equal -2, so (7,7) does not lie on the line $2y=x-9$.

#### Question 2: Does the point (3,11) lie on the line $4y=12x+8$

$$4y=12x+8$$

$$4\times11=12\times3+8$$

$$44=36+8$$

$$44=44$$

This is true, 44 does equal 44, so  the point (3,11) must lie on the line $4y=12x+8$.