Math 40 Chapter 3 Lecture Notes. Professor Miguel Ornelas
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1 Math 0 Chapter Lecture Notes Professor Miguel Ornelas
2 M. Ornelas Math 0 Lecture Notes Section. Section. The Rectangular Coordinate Sstem Plot each ordered pair on a Rectangular Coordinate Sstem and name the quadrant or ais in which the point is located. ( (, ), (0, ), (, ), (, 0),, ) ( ),, Draw a straight line that passes through points (, ) and (, ).. Is the graph of (0, ) on this line?. If ou etend the line would it pass through a point with a -coordinate of 0? The points (, ), (, ), and (, ) are three vertices of a rectangle. Find the coordinates of the fourth verte Section. continued on net page...
3 M. Ornelas Math 0 Lecture Notes Section. (continued) Right triangle ABC has legs of length. Find the coordinates of points A and B. ( 8, 7) C A B Section. Graphing Linear Equations Determine whether of the following ordered pairs are solutions to the equation. = + 7; (, ), (0, 7), (, ) Use the / table to graph the equation below. = Section. continued on net page...
4 M. Ornelas Math 0 Lecture Notes Section. (continued) Use the / table to graph the equation below. = Use the / table to graph the equation below. + = Fuel Efficienc The fuel efficienc t, in miles per gallon (mpg) of a certain truck can be approimated b t = 0.s +., where s is the speed of the truck, in miles per hour (mph).. Find the fuel efficienc when the truck is traveling at 66 mph.. At what speed will the truck have a fuel efficienc of 8.? Section. continued on net page...
5 M. Ornelas Math 0 Lecture Notes Section. (continued) Cost of College The cost T, in hundreds of dollars, of tuition and fees at the Compton Center can be approimated b T = c +, where c is the number of credits for which a student registers.. Find cost of tuition and fees when a student registers for three-credit courses.. Find the number of credits that a student can take with $,00. Section. Graphing and Intercepts Find the - and -intercepts for the line below Finding - and -intercepts To find an -intercept, let = 0 and solve for. To find a -intercept, let = 0 and solve for. Section. continued on net page...
6 M. Ornelas Math 0 Lecture Notes Section. (continued) Find the - and -intercepts for + = 6; then graph Find the - and -intercepts for = 0; then graph Find the value of C such that the graph of + C = has an -intercept of (, 0). Section. continued on net page... 6
7 M. Ornelas Math 0 Lecture Notes Section. (continued) Horizontal and Vertical Lines An equation of the form = a has a vertical line for its graph. An equation of the form = b has a horizontal line for its graph. Graph the following lines on the same rectangular coordinate sstem: =, =, and = Section. The Slope of a Line The Slope Formula (, ) (, ) Section. continued on net page... 7
8 M. Ornelas Math 0 Lecture Notes Section. (continued) Find the slope of each line Slope Formula. Find the slope of the line containing the points (0, ) and (, ).. Find the slope of the line containing the points (, ) and (, ).. Solve for the variable if the line through (, ) and (, ) has slope m =. Section. continued on net page... 8
9 M. Ornelas Math 0 Lecture Notes Section. (continued). An epress bus makes regular trips between cities. At 6:00pm, the bus is at mileage marker 0 and at 8:00pm it is at marker 70. Find the average speed of the bus.. The average amount of room, board, and tuition at a public four-ear college was $7,7 in 006 and $,89 in 00. Find the average rate at which room, board, and tuition are increasing. Graph the line with slope and -intercept Find the slope of each line whose equation is given. a. = b. = 9
10 M. Ornelas Math 0 Lecture Notes Section. Section. The Equation of a Line Slope-Intercept Form The equation of an line with slope m and -intercept b is given b = m + b Eamples. Find the equation of the line with slope and -intercept. Find the slope and the -intercept of the line with equation =. Find the slope and the -intercept of the line = 8 Graph the equation + = 6 using the slope and -intercept Section. continued on net page... 0
11 M. Ornelas Math 0 Lecture Notes Section. (continued) Point-Slope Form The point-slope form of the equation of a line is = m( ) where m is the slope of the line and (, ) is a point on the line. Eamples. Find the equation of the line with slope that contains the point (, ). Write the answer in slope-intercept form.. Find the equation of the line that passes through the points (, ) and (, ). Parallel Lines Perpendicular Lines Eamples. Find the slope of a line parallel to the line through (, ) and ( 8, ). Section. continued on net page...
12 M. Ornelas Math 0 Lecture Notes Section. (continued). Line l contains the points (, 6) and (7, ). Give the slope of an line perpendicular to l. Section.6 Graphing Linear Inequalities Graph each of the following < > Section.6 continued on net page...
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