Linear Graphs

Learning Goals & Success Criteria

Introduction to linear relations

Learning goal

By the end of the lesson I will be able to identify a linear relation from a set of ordered pairs or its equation

Success criteria

I am able to:

· identify the four quadrants on the Cartesian plane

· state the coordinates of a given point on the Cartesian plane

· state x and y intercepts from a table of values or a graph

· decide if a given point lies on a line

· find the rule that matches a table of values

· find the rule that matches a given graph

Graphing straight lines using intercepts

Learning goal

By the end of the lesson I will be able to draw the graph of a straight line using the x and y intercepts

Success criteria

I am able to:

· find the x and y intercept for linear equations given in gradient form

· find the x and y intercept for linear equations given in general form

· sketch the graph of a linear relation given its equation

· find the equation of a straight line given its x and y intercepts

· apply straight line graphs in worded problems

Lines with one intercept

Learning goal

By the end of the lesson I will be able to identify and sketch lines through the origin, horizontal and vertical lines

Success criteria

I am able to:

· identify a horizontal line and state its equation

· identify a vertical line and state its equation

· identify a line through the origin and state its equation

· sketch a horizontal line from its equation

· sketch a vertical line from its equation

· sketch a line through the origin from its equation

Gradient

Learning goal

By the end of the lesson I will be able to find the gradient of a straight line

Success criteria

I am able to:

· state the rule for gradient using rise and run

· state whether a graph has a gradient that is positive, negative, zero or undefined

· calculate the gradient given two points

· compare the gradients of graphs from their equations

Gradient and direct proportion

Learning goal

By the end of the lesson I will be able to use a straight line to represent the relationship between two variables that are directly proportional

Success criteria

I am able to:

· use a graph to find rate of change

· use an equation to find rate of change

· use a table of values to find rate of change

· represent a worded problem with a straight line equation

· use a linear relation to answer worded problems

Gradient–intercept form

Learning goal

By the end of the lesson I will be able to identify and sketch a linear graph given in gradient form

Success criteria

I am able to:

· write a linear equation in gradient form given the gradient and y-intercept.

· state the gradient and y-intercept given a linear equation in gradient form

· rearrange an equation to be in gradient form

· rearrange an equation to be in general form

· state the gradient and y-intercept given a linear equation in general form

· sketch the graph of a linear relation given in gradient form

Finding the equation of a line

Learning goal

By the end of the lesson I will be able to write the equation of a linear relation given its gradient and a point or from its graph

Success criteria

I am able to:

· find the y-intercept of a straight line given its gradient and a point

· find the equation of a straight line from its graph

· find the equation of a straight line given its gradient and a point

· find the equation of a straight line given two points

· apply the equation of a line to worded problems

Midpoint and length of a line segment

Learning goal

By the end of the lesson I will be able to find the midpoint and length of a line segment

Success criteria

I am able to:

· state the rule for finding the midpoint of a line segment

· find the midpoint between two given points

· state the rule for finding the length of a line segment

· find the length of a line segment joining two given points

· apply these rules in geometrical situations

Tasks