Slope
How do you find slope?
rise/run
y2 - y1/ x2 - x1
Solve:
2x + 5 = 23
x = 9
The solution to the system of equations:
y = -3
x = 5
(5, -3)
Define function
Having exactly one output for each input value
What makes a graph proportional?
Goes through origin (0,0)
Constant rate of change
Find the slope of the equation:
y = 3x - 6
Slope = 3
Solve:
5x - 4= x - 8
x = -1
The solution to the system of equations:
x = 4y
2x + 3y = 22
(8,2)
Evaluate the following function for f(-4)
f(x) = 3x - 4
-16
In the equation of a line, y=mx + b
What does m represent? What does b represent?
m = slope
b = y-intercept
What is the slope and y-intercept of the line
y = -7x - 6?
Slope: -7
Y-Intercept: (0,-6)
Solve:
5(x+2) = 25 + 2x
x = 5
The solution to the system of equations:
y - 3x = 3
y = 3x - 2
Evaluate the following function for f(5)
f(5)= x2 + 2x - 1
34
y = mx + b is also known as this.
Slope-Intercept Form
Write the equation of the line when
m=5 and b=13
y = 5x + 13
Solve:
x/5 + 3 = 7
x = 20
The solution to the system of equations:
y= -2x - 3
6x + 3y = -9
Infinitely Many Solutions
Function w gives the weight of a baby, in pounds, when it is m months old.
Explain the meaning of the following statement.
w(12) = 20
The baby weighs 20 pounds when it is 12 months old.
Is the point (3, -4) a solution to the equation
2y + 3x = -6?
Show OR Explain how you know!
No!
Find the slope of these two points (2,3) and (9,7)
4/7
Solve:
2(x − 10 )= 5(x + 5) - 4x
Draw/explain what one solution, no solutions and infinitely many solutions looks like
x , / /, /
Function f gives the temperature, in degrees Celsius, t hours after midnight.
Use function notation to write an equation or expression for the statement.
The temperature was the same at 9 a.m. and at 4 p.m.
f(9) = f(16)
If you are asked for the rate of change of something, what should you calculate?
Slope