The word linear has it's roots in Latin, meaning belonging to a line and a linear function means exactly that. It is a function that creates the graph of a straight line.
On a plane a straight line can be drawn in 4 ways. They can be in any direction and pass through any two points.
This means that straight lines can be:
Regardless of all different shapes all linear functions have some common characteristics.
They all have at least one intercept. Linear functions might have
The extrema behaviour of a function is a description of what happens past the viewing zone, what happens with the function outside of the area we can see.
Take this graph for example,
We can see in this graph $x$x values between $-5$−5 and $5$5, and $y$y values between $-1$−1 and $6$6. But we know that the graph goes on and on in the same linear fashion.
This is the extrema behaviour. All linear functions share the same end behaviour, with a linear function this extrema behaviour is that the line continues forever in the same direction. No kinks, turns or unexpected movement, just continues in that direction for ever.
Consider the following.
Which of the following is the graph of a linear relationship?
What makes that graph linear, but not the other two?
Consider the graph of $y=x-4$y=x−4.
State the coordinates of the $x$x-intercept in the form $\left(a,b\right)$(a,b).
State the coordinates of the $y$y-intercept in the form $\left(a,b\right)$(a,b).
If the graph is translated $6$6 units down, what will be the coordinates of the new $y$y-intercept?
State the coordinates in the form $\left(a,b\right)$(a,b).
Part of a continuous straight line graph has been graphed. Which of the following statements is true of the entire line graph (not just the graphed part).
Select all the correct options.
Determine, through investigation, the characteristics that distinguish the equation of a straight line from the equations of nonlinear relations