Lesson 18. Sloping lines

To graph a linear function:

1. Find 2 points which satisfy the equation

2. Plot them

3. Connect the points with a straight line

EXAMPLE:

y = 25 + 5x

SOLUTION:

Let x = 1 then

y = 25 + 5(1) = 30

Let x = 3 then

y = 25 + 5(3) = 40

EXAMPLE:

Draw the straight line 

y = x + 3.

Note

When working out the y-values, we usually write them in a table

Gradient

Have you ever seen sighs like this?

This is the gradient – how steep the hill is.

The “1 in 10” means that the hill goes up 1 m for every 10 m across.

Gradient = 1 in 10 = ¹/₁₀

The steeper the hill, the bigger the gradient.

EXAMPLE:

Find the gradient of this line.

EXAMPLE:

Find the gradient of this line.

Negative gradient

If a line slopes downwards to the right, it has a negative gradient.

Find the gradient of this line.negative because line sloping downwards to the right

The slope of a linear function

The steepness of a hill is called a slope. The same goes for the steepness of a line. The slope is defined as the ratio of the vertical change between two points, the rise, to the horizontal change between the same two points, the run.

The slope of a line is usually represented by the letter m. (x₁, y₁) represent the first point whereas (x₂, y₂) represents the second point.

It is important to keep the x-and y-coordinates in the same order in both the numerator and the denominator otherwise you will get the wrong slope.

EXAMPLE:

Find the slope of the line

(x₁, y₁) = (–3, –2) and (x₂, y₂) = (2, 2)

A line with a positive slope (m ˃ 0), as the line above, rises from left to right whereas a line with a negative slope (m < 0) falls from left to right,

If two lines have the same slope the lines are said to be parallel.

You can express a linear function using the slope intercept form.

y = mx + b

m = slope

b = y – intercept 

Lesson 18

•  Test 1 
•  Test 2
•  Test 3