Interactive practice questions
The graphs of the equations $y=x+1$y=x+1, $y=2x+1$y=2x+1 and $y=4x+1$y=4x+1 are shown below on the same number plane.
What do all of the equations have in common?
The constant is the same.
The coefficient of $x$x is the same.
They are all written with $x$x as the subject of the equation.
What do all of the graphs have in common?
All of the graphs cross the $x$x-axis at the same point.
All of the graphs have the same slope.
All of the graphs cross the $y$y-axis at the same point.
What can you conclude from the answers above?
Equations of the form $y=ax+b$y=ax+b that have the same value of $b$b generate graphs that cross the $x$x-axis at the same point.
Equations of the form $y=ax+b$y=ax+b that have the same value of $b$b generate graphs that cross the $y$y-axis at the same point.
Equations with the same $x$x-intercept generate graphs that cross the $y$y-axis at the same point.
Equations with the same constant term generate graphs that have the same slope.
What is the $y$y-intercept of the line $y=-x+6$y=−x+6 ?
What does $b$b represent in the equation $y=ax+b$y=ax+b?
Look at the graph of the line.