Gradient

We now know three different ways to identify the gradient of a line. Let’s remind ourselves what those ways are for the line 2x + y = 6.

**Parallel lines** are lines which have the same gradient.

**Perpendicular lines ** are lines whose gradients are at right-angles. If two lines are at right-angles, **the product of their gradients will be -1**.

**Exercise**

Let’s complete questions 1 to 4 of exercise 14F on page 227 of the textbook

The answers are below:

**y=mx+c equation**

We saw earlier that when an equation is written in the form y=mx+c, the m tells us the gradient of the equation. But what about the c? Well what happens if we substitute x=0 into the equation? What does this tell us in terms of the graph?

**Exercise**

Let’s complete exercise 14G on pages 228 and 229 of the textbook:

The answers are below:

Everything we have done so far here has been **abstract**, i.e. looking at equations with unknowns, but not relating it to word problems. Now let’s try applying some of these technical skills to word problems.

**Exercise**

Let’s complete exercise 14H on pages 229 to 231 of the textbook:

The answers are below: