Economics 201- Lab 11. Graphing Definitionsa. Independent vs. Dependent VariablesIndependent variables do not rely on other variables in order to changeDependent variables only experience a change in response to a change in another variable (the independent variable)b. Slope: Positive vs. NegativeSlope Rise over run; the rate at which the variables alter in regards to one anotherPositive Slope is when the X and Y are both increasing or decreasing togetherNegative Slope happens when one increases as the other decreases2. Functions, Schedules, and GraphsY=10+5XFirst, make your X-Y chart Second, sketch your graph1 2 3 4 50510152025303540 Next, calculate your slope, y-intercept, independent variable, and dependent variable.Slope=Rise/Run=5/1=5Y-Intercept=where the line crosses Y=10Independent Variable=XDependent Variable=YX Y1 152 203 254 305 353. Rates of ChangeWhat happens when the rate that Y changes is not held constant?a. Below are four common instances where the Y variable and X variable do not change at constant speeds. Graph each one. The description above the graph refers to the Y variable.Exponential functions: Logarithm functions: Increasing at increasing rate increasing at decreasing rateDecreasing at increasing rate Decreasing at decreasing rateNow, let’s discuss each graph.Increasing at Increasing Rate: As the variable X increases, the gap between each Y variable decreases and the numerical values increase, causing an exponential curve of the graph.Increasing at Decreasing Rate: As the variable X increases, the gap between each Y variable increases and the numerical values increase, causing a logarithmic curve of the graph.Decreasing at Increasing Rate: As the variable X increases, the gap between each Y variable decreases and the numerical values decrease, causing a downward curve of the graph.Decreasing at Decreasing Rate: As the variable X increases, the gap between each Y variable increases and the numerical values decrease, causing and inverted downward curve of the graph.4. Shifts in the CurveEvery 10 years, the US Census conducts an enormous national survey, collecting various socioeconomic data. One item is median annual income, level of educational attainment,and age. The table below shows the data (incomes in 1999). Use it to graph median annual income by age.Median Income By EducationAge HS Graduate College Grad Advanced Degree21-24(22) $20,000 $27,000 ---25-34(30) $25,500 $37,000 $43,00035-44(40) $29,000 $49,000 $59,00045-54(50) $30,000 $49,000 $59,00055-64(60) $30,000 $50,000 $60,00065-74(70) $23,000 $42,000 $56,000Median Annual Income70,00055,000 Advanced Education40,000 College Education25,000 High School Education10,000 10 20 30 40 50 60 70 AGE5. Interpreting GraphsInterpret the graph above: The higher education level an individual receives, the greater amount of income that individual will make. All three levels of education, shown above, experience a decrease at an increasing rate once the individual turns 60 years old.6. Graphing on your ownHow might you graph your test scores by hours of study? Exam GradeHours of StudyThe more hours an individual studies usually results in higher exam averages. However, every individual reaches a max point at which he or she no longer retains information and begin to suffer from lack of sleep, which will result in lower test grades. The graph can be drawn increasing at a decreasing