The GradientAlgebra – Linear Functions

By the end of this lesson you will be able to identify and calculate the following:1. Find the gradient of a line from the graph

Morning Math:

The Cartesian plane consists of 2 axesi) ii)

The order that the coordinates are written is the ___coordinate first and then ___coordinate.

Points can be plotted byi) ii)

Determine which of the following is a linear grapha) y= x4 + 15 b) 6y + 3x= 18

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General equation of a straight line

Any equation of a straight line can be written in the form y = mx + c, where m and c are constants.

This is known as the general equation, or the standard form of a linear rule.

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The gradient of a straight line is a measure of the steepness of that line. The gradient is often referred to as the ‘slope’. The steeper the hill the greater the gradient.

Positive Gradient-from left to right, the slope is upwards=positive gradient

Negative Gradient-from left to right, the slope is downwards=negative gradient

The Gradient

In this section we will consider three methods of finding the gradient of a line:

Method 1- From the graph

Method 2- From the coordinates of any two points on the line

Method 3- From the rule.

The Gradient-METHOD 1

METHOD 1- Finding the gradient of a line from the graph

Step 1 Draw a right-angled triangle (called ‘gradient triangle’) anywhere along the line.

Step 2 Use the triangle to measure the vertical distance (called the ‘rise’) and the horizontal distance (called the ‘run’).

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Step 3 Calculate the ratio of the vertical distance to the horizontal distance to find the value of the gradient.

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Observe that in the previous worked example (a), the graph that sloped upward to the right had a positive gradient, while the graph (b) which sloped downward to the right had a negative gradient. Finally (c), a horizontal line had a gradient of 0.

These observations will hold for any linear graph.

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Your turn…

Complete - Questions 1 all - Skill Sheet 6.5

Exercises and Skill Sheet are in your Booklet

All questions are to be answered in your math book!

The Gradient

Homework!

HOMEWORK!!!

Complete - Questions 1 all (a – l)

All questions are to be answered in your math book!