Slope Changes the Steepness
What part of the equation y=mx+b controls how steep the line is?
What is the slope?
In the equation y=mx+b, what does the b represent?
What is the y‑intercept?
Changing the equation from y=x to y=x+3 causes what transformation?
A shift up 3 units.
Which line is steeper: y=4x or y=2x?
What is y=4x?
Where does the line y=2x+5 cross the y‑axis?
At (0, 5).
Changing the equation from y=x to y=x−4 causes what transformation?
A shift down 4 units.
If the slope changes from 1 to 5, what happens to the steepness?
It becomes steeper.
Do two lines with the same slope but different y‑intercepts ever touch?
No, they are parallel.
Does shifting a line up or down change its slope?
No, the slope stays the same.
Does a slope of −3 rise or fall as you move right?
It falls (negative slope goes downward).
What is the y‑intercept of the line y=−3x−7?
What is -7?
How far does the line shift when going from y=2x+1 to y=2x−6?
It shifts down 7 units.
Which line is flatter: y=12x or y=3x?
What is y=1/2x?
How does changing the y‑intercept affect the steepness of a line?
It does not change steepness, only the starting point.
What part of the equation must change for a vertical shift to occur?
The y‑intercept.