LINEAR GRAPHS AND FUNCTIONS UNIT ONE GENERAL MATHS

INTRODUCTION TO LINEAR GRAPHS A linear function or equation is a set of ordered pairs that, when graphed, form a straight line. What does a Linear Graph look like?

DETERMINING THE EQUATION OF A STRAIGHT LINE gradient The ‘steepness’ of the line

SKETCHING A STRAIGHT LINE

(0, 1) (2, 4)

SKETCHING A STRAIGHT LINE (0, 0) (1, 2 ) (2, 4 ) (3, 6 ) (-1, -2 ) We could plot more points in this manner…..

SKETCHING A STRAIGHT LINE (0, 2) (1, 6)

SKETCHING A STRAIGHT LINE

(0, 2) (3, 0)

SKETCHING A STRAIGHT LINE (0, 4) (-2, 0)

SKETCHING A STRAIGHT LINE (0, 9) (3, 0)

SKETCHING A STRAIGHT LINE (0, 4)

NOW DO – WORKSHEET ONE

SKECTHING A STRAIGHT LINE

Enter one equation into y1, the other to y2. Highlight and drag each into the graph.

SKECTHING A STRAIGHT LINE

NOW – CHECK YOUR ANSWERS FROM WORKSHEET ONE WITH THE CLASSPAD

DETERMINING THE EQUATION OF A STRAIGHT LINE gradient The ‘steepness’ of the line

THE GRADIENT OF THE GRAPH

DETERMINING THE EQUATION OF A STRAIGHT LINE

DETERMINING THE GRADIENT AND Y-INTERCEPT Gradient = 5 y-intercept = 2 Gradient = -3 y-intercept = 7

DETERMINING THE GRADIENT AND Y-INTERCEPT Gradient = 3 y-intercept = 1 Gradient = -3 y-intercept = 4

DETERMINING THE GRADIENT GIVEN 2 POINTS

THE GRADIENT OF THE GRAPH

NOW DO – EXERCISE 10B Q1,2,3,5,6,9,10AC,12,13,16,17,19,20,21,24

DETERMINING THE EQUATION OF A LINE

DETERMINING THE EQUATION OF A STRAIGHT LINE

FINDING THE EQUATION OF A LINE GIVEN 2 POINTS

Bivariate Data can be displayed on a scatterplot. What does this look like? Two sets of data that is related is given on a table. This data is used as sets of coordinates. We plot these on an axis and use it to model relationships between variables. DISPLAYING DATA ON A SCATTERPLOT

Age (years) Foot length (cm) Example: Plot the following data on a scatterplot.

Once the data is plotted on the graph, we can add a line of best fit to model the data. How to add a line of best fit Fit the line ‘by eye’ by balancing the data points on either side of the line. DRAWING A LINE OF BEST FIT ON A SCATTERPLOT

How to add a line of best fit Fit the line ‘by eye’ by balancing the data points on either side of the line. DRAWING A LINE OF BEST FIT ON A SCATTERPLOT

FINDING THE EQUATION OF A LINE OF BEST FIT

(1.5, 65) (4, 85)

USING THE LINE OF BEST FIT TO MAKE PREDICTIONS Once we have a line of best fit, we can use this to make predictions. We can make predictions using either the graphed line – reading off the graph; or by substituting values into the linear equation and solving. Example: Estimate how many hours a student worked to obtain a grade of 80 Reading off the graph = 3.5 hours

USING THE LINE OF BEST FIT TO MAKE PREDICTIONS

RELIABILITY OF PREDICTIONS For the graphed data shown right, the data is plotted and shown in the range between the dotted lines. When making predictions, estimates that fall in this range is called INTERPOLATION – these predictions are reliable, as the line is based on data in this range. Any predictions made relating to data outside of this range is called EXTRAPOLATION – these predictions are not reliable, as the line is based on data outside of this range.

When making predictions, estimates that fall in this range is INTERPOLATION – these predictions are reliable. Any predictions made relating to data outside of this range is EXTRAPOLATION – these predictions are not reliable. eg1. If I use the line to predict what test score someone got in Physics, based on a score of 60 in Maths – would this be a reliable prediction? YES – Interpolation eg2. If I use the line to predict what test score someone got in Physics, based on a score of 25 in Maths – would this be a reliable prediction? NO – Extrapolation

NOW DO – EXERCISE 10D Q1, 2, 3, 5, 6, 8, 10, 11, 13, 14,15A, 16, 17, 18