- Date:08 Apr 2020
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In the figure above,1 What are the coordinates of point A. 2 What are the coordinates of point D,3 What are the coordinates of point E. 4 What are the coordinates of point H, 5 Which of the following best describes a triangle in the standard x y coordinate plane with. vertices at 0 0 3 5 and 0 2,A All three angles measure less than 90. B All three sides are the same length,C Exactly two sides are the same length.

D One angle measures 90,E One angle measures more than 90. 6 In the standard x y coordinate plane shown below two circles of the same radius r are. enclosed by rectangle ABCD Which of the following expressions is equal to a b. The Cartesian plane is divided into four,quadrants These are numbered from I. through IV starting with the upper right and,going around counterclockwise For some. reason everybody uses roman numerals for,this In Quadrant I both the x and y. coordinates are positive in Quadrant II the x,coordinate is negative but the y coordinate is.

positive in Quadrant III both are negative,and in Quadrant IV x is positive but y is. Points which lie on an axis i e which have at,least one coordinate equal to 0 are said not. to be in any quadrant Coordinates of the,form x 0 lie on the horizontal x axis and. coordinates of the form 0 y lie on the vertical y axis. In the figure above,7 In which quadrant is point B. 8 In which quadrant is point C,9 Which points are in quadrant IV.

10 Which points are in quadrant III, 11 The following standard coordinate plane is shown with the four quadrants labeled Point R. denoted by R x y is graphed on this plane such that x 0 and y 0. If the product xy is a negative number then point R is located in. A Quadrant I only,B Quadrant II only,C Quadrant III only. D Quadrant II or IV only,E Quadrant I or III only, 12 Rectangle ABCD is graphed in the x y coordinate plane below What fraction of rectangle ABCD. lies in Quadrant IV,Linear functions, A function relates an input to an output It is like a machine that has an input and an output and the. output is related somehow to the input The classic way of writing a function is f x Like this f x x 1. It can be written as a table to show the relationship between the input and the output To find the f x. simply choose some values for x and plug them into the equation On a coordinate plane rather than. writing the function as f x we usually write y like this y x 1 Either way it s written is okay. x f x or y, 13 A particular linear equation includes the x pairs below What is the value of b.

x f x or y,Introduction to linear equations, Linear equations are functions that can be represented as a line on a graph The x value is the input and. the y value is the output It works sort of like this When we have a question like this 1 7 Y I know. the answer is 8 But if I have a question like this 1 X Y The answer is it depends because there is. more than one possible answer For example if X 0 then Y would be 1 but if X 5 then Y would be 6. There are an infinite number of possible answers There is a way to find all the possible answers very. quickly Because Y depends on what we choose for X there is a relationship that can be written as a line. on a coordinate plane, A linear equation in two variables describes a relationship in which the value of one of the variables. depends on the value of the other variable In a linear equation x is the independent variable and y is. the dependent variable When you assign a value to the independent variable x you can compute the. value of the dependent variable y You can then plot the points named by each x y pair on a. coordinate grid, The good news is that if you know 2 points you can draw a line that includes all the other possible. answers So finding many pairs of values that satisfy a linear equation is easy Find two pairs of values. and draw a line through the points they describe All other points on the line will provide values for x. and y that satisfy the equation, For example the equation 3x 2y 6 is a linear equation To find all the possible solutions we need to. find at least 2 answers Since any two will do I prefer to pick easy ones If x 0 then y has to be 3 We. have our first possible answer We write this as an ordered pair 0 3 If y 0 then x has to be 2 We. have a second possible answer We write this as an ordered pair 2 0 Making a line through those two. points give us all the possible answers for the equation. 14 Graph the line X Y 3 on the grid at the right,15 Graph the line 2X Y 4 0 on the grid.

16 Graph the line Y X 3 on the grid,Example of linear relationships. Distance rate x time, In this equation for any given steady rate the relationship between distance and time will be linear. However distance is usually expressed as a positive number so most graphs of this relationship will only. show points in the first quadrant Notice that the direction of the line in the graph below is from bottom. left to top right Lines that tend in this direction have positive slope A positive slope indicates that the. values on both axes are increasing from left to right. In the example above the rate is 25 miles per 1 hour This rate is called the slope of the line. The slope tells you two things how steep the line is with respect to the y axis and whether the. line slopes up or down when you look at it from left to right If the slope is positive then the. line slopes up from left to right If the slope is negative then the line slopes down from left to. right It is written like this or In the example above it would be. When you re plotting data slope tells you the rate at which the dependent variable is changing. with respect to the change in the independent variable It may have a positive slope where y is. increasing as x is increasing it may have a negative slope where y is decreasing as x is. increasing it may have a horizontal slope where y remains the same as x is increasing or it may. have a vertical slope The slope of a vertical line is called undefined. Below is the graph that a specialty automobile manufacturer uses to plot the speed tests done. on his new cars The speed is recorded in units of and is conducted for a period of 9 seconds. 17 From 0 to 4 seconds the speed is,a increasing,b constant. c decreasing,18 From 4 to 7 seconds the speed is,a increasing. b constant,c decreasing,19 From 7 to 9 seconds the speed is.

d increasing,e constant,f decreasing, The recreation center has installed a swimming pool on level ground The pool is a right. circular cylinder with a diameter of 24 feet and a height of 6 feet A diagram of the pool and. its entry ladder is shown below, Two hoses are used to fill the pool Twice as many gallons of water per minute flow. through one of the hoses as through the other Both hoses had been on for 12 hours and. had filled the pool to the 4 foot mart when the hose with the faster flow stopped working. The hose with the slower flow then finished filling the pool to the 5 foot mark Which of. the following graphs shows the relationship between the time spent filling the pool and the. height of the water in the pool,Using two points to find the slope. In mathematics the slope of a line is often called m We can find the slope if we have two. points on the line We ll call the first point and the second point To find the. slope we make a fraction Take the y value from the second point and subtract the y value from. the first point for the numerator and take the x value from the second point and subtract the x. value from the first point for the denominator, The slope of the line that contains the points A 2 3 and B 0 1 is. The slope of the line that contains the points A 2 3 and B 0 1 is. 20 What is the slope between 0 0 and 4 3,21 What is the slope between 3 7 and 4 2.

22 In the coordinate plane a line runs through the points 3 3 and 2 5 What is the slope. of the line, 23 In the Cartesian plane a line runs through the points 6 7 and 2 9 What is the slope. of the line, For a chemistry class Kaleb is doing an experiment that involves periodically heating a. container of liquid The graph below shows the temperature of the liquid at different times. during the experiment Use the graph to answer the following questions. 24 What is the rate of change from 0 minutes to 5 minutes. 25 What is the rate of change from 5 minutes to 7 minutes. 26 What is the rate of change from 7 minutes to 10 minutes. 27 What is the rate of change from 15 minutes to 17 minutes. 28 What is the average rate of change of temperature in degrees Celsius per minute. during the times in which Kaleb is applying heat to this container Hint What is the. total rise in temperature What is the total time where heat was applied The average. will be the total rise in temperature divided by the time heat was applied. Slope Intercept Form, The equation of a line can be written many different ways The following are all linear equations. 2x y 3 x y 5 0 x y 3x 2, Each of these can be represented as a line on a graph However there is one form that is the most. useful form for linear equations It is called the slope intercept form and it looks like this. For example in the equation y x 3 the m or slope in the equation would be and the b or y. intercept would be 3 The m value is the slope and the b value is the y intercept The y intercept is. the point where the line crosses the y axis In the graph below the y intercept is 3. When graphing an equation in slope intercept form the y intercept gives the first point If the y. intercept is 3 then put a point on the 3 on the y axis From there the slope tells where to put the next. point The numerator tells how far up or down to move and the denominator tells how far to move to. the right For example if the slope is then you go up 1 and to the right 2 If the slope is negative. for example then you move down 2 and to the right 3 If the slope is a whole number convert it to a. fraction For example 2 is the same as which means you move up 2 and to the right 1 and 5 is the. same as which means you move down 5 and to the right 1. 29 What is the slope of the line y X 3,30 What is the slope of the line y X 3.

31 What is the slope of the line y X 7,32 What is the slope of the line y 7X 2. 33 What is the slope of the line y X 5,34 What is the slope of the line y X 13. 35 What is the slope of the line y X 4,36 What is the slope of the line y X 3. 37 What is the y intercept of the line y X 3,38 What is the y intercept of the line y X 3. 39 What is the y intercept of the line y X 3,40 What is the y intercept of the line y X 7.

41 What is the y intercept of the line y 7X 2,42 What is the y intercept of the line y 2X. 43 What is the y intercept of the line y 7X 12, 44 Which of the following is an equation for the graph in the following standard x y coordinate. 45 Which of the following equations represents the linear relation shown in the standard x y. Math 1 packet for Coordinate Geometry part 1 Reviewing the basics Ordered pairs coordinates The location of a point in the plane is given by its coordinates

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