Linear Functions (Guided Lesson)

Definition

Definition

• m is the variable representation for slope

• b is the variable representation for the y-intercept

Definition

The y-intercept is the y-coordinate of the point where the graph of a relation intersects the y-axis.

The y-intercept can be written as a coordinate point! The y-intercept on this graph is (0, 4). Notice that for the y-intercept, the value of the x coordinate is 0. This will always be true!

The slope of a line is a measure of its steepness and direction. A line that rises from left to right has positive slope. A line that falls from left to right has negative slope. Look at slope guy Bob!

Count!

rise

run

Now, that you know what the slope is

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1) Find two coordinate points on the graph.

2) Label each point as 1 or 2.

3) Substitute into the slope formula.

4) Calculate the slope.

• Coordinate point 1________________

• Coordinate point 2 _______________

• x₁ = _{__________________}

• x₂ = ______________

• y₁= ______________

• y₂= ______________

Now, you understand how to find the slope, m, and the y-intercept, b.
This means that you know how to create a linear function from a graph.

To graph a linear function, you need a minimum of two points. More points the better but you only need two! Follow the steps below:

1) Plot the y-intercept first

2) Use the slope as a road map to find the second point

3) Use the slope to find another point

Clear your desk. Put all notes away

This will count as an assessment grade.