concept map for chapters 1, 2, and 7.1

concept map for chapters 1, 2, and 7.1

1. relation: any set of ordered pairs. example would be a list of x's and y's

   • each input should have exactly 1 output and 2 different inputs shouldn't get the same output

2. linear model: an equation of the form y= mx+b

   • m = slope
     • m = rate of change
   • b = the y intercept
     • the y intercept stands for when x is zero, the y intercept is where the line goes through y
   • y= 4x + 6
     • x=0 then y=6
       • 6 is the y intercept
     • 4 is the slope

3. function: a relation in which each input gives exactly 1 output

4. vertical line test: graph of a function if and only if no vertical line interests the graph more than once

   • no y's can be the same

5. net change: the value of a function

6. domain is x

   • range is y
     • the function decreases if the value of y decreases as x increases
     • y is the horizontal line
   • the function is increasing if the value of y increases as x increases
   • x is the vertical line

7. average rate of change: net change in y / change in x

   • f(b) - f(a) / b - a

8. average speed of a moving object: net change in distance / change in time

9. slope = rise / run

   • y2 - y1 / x2 - x1

10. point-slope for of the equation of a line

    • y - y1 = m(x - x1)

11. general form of the equation of a line

    • Ax + By + C = 0

12. parallel lines: if slopes are the same

    • m1 = m2

13. perpendicular lines

    • m1 = -1 / m2

14. constant of probability

    • y = kx