Linear Relationships coordinates reflections origin non-linear relationship continuous gradient plot rotations magnitude increasing scale linear equation Cartesian plane image decreasing derive intersecting point transformation pattern pronumeral parallel perpendicular solution translations table of values graph

Graphing points on the Cartesian Plane

Number Patterns

Using Patterns

Graphing Lines

Finding the Equation of a Line A rule must be true for every pair of coordinates (x, y) in a table or graph. coefficient of x constant y = □ × x + □ Consider a linear rule of the form y = □ × x + □. The coefficient of x will be the increase in y as x increases by 1. If there is a decrease in y, then the coefficient will be negative.

Finding the Equation of a Line

Using Intercepts to Sketch a Line

Solve the equation 4 - x = 2x + 1. Intersection of Lines Solve the equation 4 - x = 2x + 1.

For each of these graphs write down the coordinates of the point of intersection (i.e. the point where the lines cross over each other).

Non-Linear Relationships a Use this graph of y = x2 to solve the following equations. b Explain why there are two solutions to each of the equations in question a above. c Give one reason why the graph of y = x2 does not give a solution to the equation x2 = -9. d Graph y = x + 2 and y = x2 on the same screen and graphically solve x2 = x + 2 by finding the x values of the points of intersection.