10.01 Equations of parallel and perpendicular lines
Interactive practice questions
The equations $y=2x$y=2x, $y=2x+6$y=2x+6 and $y=2x-8$y=2x−8 have been graphed on the same number plane:
What do all of the equations have in common?
Their $y$y-intercept ($b$b)
Their slope ($m$m).
Their $x$x-intercept.
What do you notice about the graphs?
All graphs cut the $y$y-axis at the same point.
All graphs cut the $x$x-axis at the same point.
All graphs have the same angle of inclination.
What can you conclude from the answers above?
Equations with the same $x$x-intercept have graphs that have the same angle of inclination.
Equations with the same slope ($m$m) cut the $y$y-axis at the same point.
Equations with the same slope ($m$m) have graphs that have the same angle of inclination.
Equations with the same $y$y-intercept ($b$b) have graphs that have the same angle of inclination.
Is the line $y=4x-1$y=4x−1 parallel to $y=4x-6$y=4x−6 ?
Is the line $y=-8x-2$y=−8x−2 parallel to $y=9x+7$y=9x+7 ?
Are the lines $y=-6x-5$y=−6x−5 and $y=x$y=x parallel?