Interactive practice questions
The graphs of the equations $y=x+3$y=x+3, $y=2x+3$y=2x+3 and $y=4x+3$y=4x+3 are shown below on the same number plane.
What do all of the equations have in common?
The coefficient of $x$x is the same.
They are all written with $x$x as the subject of the equation.
The constant is the same.
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 gradient.
All of the graphs cross the $y$y-axis at the same point.
What can you conclude from the answers above?
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 gradient.
Equations of the form $y=mx+c$y=mx+c that have the same value of $c$c generate graphs that cross the $x$x-axis at the same point.
Equations of the form $y=mx+c$y=mx+c that have the same value of $c$c generate graphs that cross the $y$y-axis at the same point.
What is the $y$y-intercept of the line $y=-x+6$y=−x+6 ?
What does $c$c represent in the equation $y=mx+c$y=mx+c?
Look at the graph of the line.