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

 The Cartesian plane consists of 2 axes i) ii)  The order that the coordinates are written is the ___coordinate first and then ___coordinate.  Points can be plotted by i) ii) Determine which of the following is a linear graph a) y= x b) 6y + 3x= 18

 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.

 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

 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.

 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’).

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

 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.

 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!

 HOMEWORK!!!  Complete - Questions 1 all (a – l) All questions are to be answered in your math book!