1. Linear Models

2. Functions n function - a relationship describing how a dependent variable changes with respect to an independent variable n dependent variable - a variable taken as the outcome of one or more other variables n independent variable - the variable that is manipulated by the investigator

3. Functions (cont.) n We express the function as: (independent variable, dependent variable) or (x, y)

4. Example Independent variable = time Dependent variable = temperature (time, temperature)

5. Linear Models n Linear models - a function with a constant rate of change n rate of change = slope n slope = change in dependent variable change in independent variable Y2 – Y1 m = ---------- X2 - X1

6. Linear Models n y = mx + b where m = slope; b = y intercept n The greater the rate of change (slope), the steeper is the graph b

7. How to draw a graph n Identify the independent and dependent variables. –Place the independent variable on the x- axis (across the bottom) –Place the dependent variable on the y-axis (up and down) –Graphs are always made y vs. x

8. How to draw a graph (cont.) n Identify the domain and the range –domain = the spread of the independent variable –range = the spread of the dependent variable n Draw the y and x axis –The divisions should be evenly spaced –Pay attention to the domain and range

9. How to draw a graph (cont.) n Plot your points n Draw a best fit line through the data –Do not connect the dots –The data points should be evenly spaced above and below the axis

10. How to draw a graph (cont.) n Determine the slope of the graph –Pick two points that fall ON THE LINE –Note: these points do not need to be data points –slope =  y/  x

11. How to draw a graph (cont.) n Determine the equation of the line –remember y = mx + b –m = slope –Pick one of the points that fell on the line –Plug the y, x, and m values in –solve for b n Now you know the equation!