Slope Basics
What is slope?
Answer: Rise over run; the rate of change.
A linear graph is a…
Answer: Straight line
In y=mx+by=mx+by=mx+b, what is b?
Answer: The y-intercept (starting point).
What’s the formula for a linear equation?
Answer: y=mx+b
What is the slope formula?
(y_2-y_1)/(x_2-x_1)
If a line goes down from left to right, the slope is…
Answer: Negative.
A non-linear graph is usually…
Answer: Curved (not a straight line).
In y=mx+by=mx+by=mx+b, what is m?
Answer: Slope (rate of change).
A line has slope m=5 and y-intercept b=−2. Write the equation.
Answer: y=5x−2
Find the slope between (2,3) and (4,7).
4/2=2
A line has rise = 6 and run = 3. What is the slope?
Answer: 6/3=2
Using the arrow test: if arrows go up from left-to-right, the function is…
Answer: Increasing.
Graph y=2x+1. What is the y-intercept?
Answer: b=1 → point (0,1)
A line crosses the y-axis at 7 and goes down 2 for every 1 right. Write the equation.
Answer: m=−2, b=7 → y=−2x+7
Find the slope between (−1,5) and (3,5).
0
A line has rise = -4 and run = 2. What is the slope?
Answer: −4/2=−2
If a function has a constant rate of change, it is…
Answer: Linear.
Graph y=−1/2x+4. After plotting (0,4) what is the next point using slope?
Answer: Down 1, right 2 → (2,3)
A proportional relationship always has what y-intercept?
Answer: b=0 (it passes through the origin).
Find the slope between (6,2) and (6,−4).
Undefined (division by 0); vertical line.
What does slope m=0m=0m=0 look like on a graph?
Answer: A horizontal line.
A graph increases, but is curved (rate changes). It is…
Answer: Increasing and non-linear.
If the slope is 3/4, what “moves” do you use?
Answer: Up 3, right 4.
Which is proportional: y=3x or y=3x+2? Why?
Answer: y=3x because b=0 and it goes through (0,0)
Write an equation through the points (1,2) and (3,8).
m=3, b=1, y=3x−1