Linear Function :(Module): Sharmaine N. Sayao Mathematics IV-A Mrs. Imelda Sayao 1.1 Definition of a Linear Function A linear function is a function whose graph is a straight line. The equation of a linear function of x can be written in the form f(x) = mx + b or a linear equation y = mx + b where m is the slope and b is the y-intercept. The equation in the form Ax + By = C where A‚ B and C are real numbers is referred to as the general form of a linear equation. We
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represents the heights that are achieved by the gold medalists. Also it shows that it is not constant. Linear Regression To create a certain equation‚ you draw the best fit line on the graph. The difference between the red graph and the linear function is that the red does not have a predictable pattern. When the best fit is drawn it is possible to find the equation of this graph. Though the equation that is made by the best fit and three points on the graph is actually on the line‚ there is a limit
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outliers in the graph and it has been a pretty steady linear rise. The type of function that models the behavior of the function is linear. This type of function models it because the points resemble a line rather than a curve. To represent the points plotted in Data Graph 1 a function is created. To start deciphering a function I started with the equation - Y = mx + b To show the slope of the line since the function is linear. For the first point the function would have to satisfy
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WEST AFRICAN SENIOR SCHOOL CERTIFICATE EXAMINATION FURTHER MATHEMATICS/MATHEMATICS (ELECTIVE) AIMS OF THE SYLLABUS The aims of the syllabus are to test candidates on: (i) (ii) (iii) further conceptual and manipulative skills in Mathematics; an intermediate course of study which bridges the gap between Elementary Mathematics and Higher Mathematics; aspects of mathematics that can meet the needs of potential Mathematicians‚ Engineers‚ Scientists and other professionals. EXAMINATION FORMAT There will
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Concentration of bromophenol blue (mg/L) 0.0 2.0 4.0 6.0 8.0 10.0 Absorbance at 590 nm (Amax of bromophenol blue) 0.000 0.135 0.199 0.404 0.596 0.724 From Figure 2 above‚ the molar absorptivity of bromophenol blue at 590nm is the gradient of the linear regression line which is 0.0744 L mg-1 cm-1. Part 3: Determination of the concentration of the bromophenol blue solutions of unknown concentration By plotting on the standard concentration curve from Part 2‚ the concentration of bromophenol blue
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from now" is six times Miguel’s "age last year" or‚ in math: g + 3 = 6(m – 1) This gives me two equations with two variables: m + g = 68 g + 3 = 6(m – 1) Solving the first equation‚ I get m = 68 – g. (Note: It’s okay to solve for "g = 68 – m"‚ too. The problem will work out a bit differently in the middle‚ but the answer will be the same at the end.) I’ll plug "68 – g" into the second equation in place of "m": g + 3 = 6m – 6 g + 3 = 6(68 – g) – 6 g + 3 = 408 – 6g – 6 g + 3 = 402 – 6g
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completed worksheet. Question 1: What trend does the graph illustrate? (2) 4. After the graph is complete‚ right-click on one of the data points on the graph. Select ‘Add trendline” 5. Choose “Linear” for the trend/regression type. Then at the bottom of the window‚ select “display equation on chart” and “Display R-squared value on chart”. Question 2:
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Section 2.3 Linear Functions and Slopes 1 Section 2.3 Linear Functions and Slopes The Slope of a Line 2 Section 2.3 Linear Functions and Slopes Find the slope of the line that passes through (-2‚5) and (3‚-1) change in y 5 1 6 6 m or change in x 2 3 5 5 3 Section 2.3 Linear Functions and Slopes 4 Section 2.3 Linear Functions and Slopes Example Find the slope of the line passing through the pair of points (5‚-2) and (-1‚7). 5 Section 2.3 Linear Functions and Slopes First:
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Grant Center assumes a linear relationship between the number of student visitors and the daily operating cost of the center. Some sample (number of students‚ operating cost) values are given in the table below. Number of Students 0 10 20 40 Daily Operating Cost $450 $600 $750 $1‚050 a. Use the given data to write an equation showing how operating cost‚ C‚ depends on the number of students‚ x. Explain or show how you found the equation. For parts (b)–(d)‚ write equations or inequalities for
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Exam Notes Unit 1 The Method of Substitution -Solving a linear system by substituting for one variable from one equation into the other equation -To solve a linear system by substitution: Step 1: Solve one of the equations for one variable in terms of the other variable Step 2: Substitute the expression from step 1 into the other equation and solve for the remaining variable Step 3: Substitute back into one of the original equations to find the value of the other variable Step 4: Check
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