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: