A) Find an equation of a straight line, in terms of well defined constants, in order to investigate the validity of this assumption b) Plot a suitable graph to show that the assumption of part (a) is valid c) Use the graph of part (b) to estimate, correct to 1 decimal place, the value of a and the value of b d) Estimate the value of y when xThe graph is the straight line that passes through those two intercepts Example 2 Mark the x and y intercepts, and draw the graph of 5 x − 2 y = 10 Solution Although this does not have the form y = ax b, the strategy is the same Find the intercepts by putting x then y equal to 0 xQ Which of these lines will intercept the yaxis at 5?
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How do you graph the line y=x-This strand of the inquiry developed out of graphing the equation when students asked what happened to the straight line when it got to (0, 4) The comment about x and y taking any value led to a discussion about dependent and independent variables, while the one on the use of x and y developed into considering conventions in mathsSuch an equation is usually written y=mxb ("y=mxc" in the UK) "y=mxb" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis The X and Y intercepts and the Slope are called the line properties We shall now graph the line yx3 = 0 and calculate its properties
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Straight line graphs Lessons 12 Essential Knowledge Teaching Points Use function machines to find coordinates (ie given the input x, find the output y); Subtract x from both sides to get y = 6 −x Put in values for x and calculate corresponding values of y Example x = 1 gives y = 5 x = 10 gives y = −4 Since it is the equation of a straight line you only need to find to points, then draw a straight lint between them Answer linkSolution Steps y = x2 y = x − 2 Swap sides so that all variable terms are on the left hand side Swap sides so that all variable terms are on the left hand side x2=y x − 2 = y Add 2 to both sides Add 2 to both sides
Plotting Straight Line Graphs If you need to draw a straight line graph, here is an easy method of how to do it Write down 3 values for x you want to use I like to use 2, 0, 2 Work out the value for y with these x values Plot the coordinates on the graph Check your points are perfectly straight and use a ruler to draw the line through themCalculate gradients and intercepts of the graphs and then plot them to check Solve problems involving direct and inverseConsider the following 2 facts 1 In real life, every time 12 hours passes, the bacteria increase by a factor of 10 2 In math life, every time you move up a log unit, you're increasing the magnitude of the
X = 4 Make your own Graphs Explore the Quadratic Equation Graph Equation of a Straight Line Find the Line Equation From 2 Points The graph of an equation in the form y=mx b is a straight line Can the equation of every straight line be written in the form y=mx b (Hint What is the equation of a vertical line?) math If two quantities vary directly, which must be true of a graph showing the relationship between them?Section A Plotting Straight Line Graphs Grade D / C 1 (a) Complete the table of values for y = 3x 4 x 0 1 The graph y = x2 – 2x – 4 is drawn below for values of x between –3 and 4 (a) Using the graph, find the solutions of x2 – 2x – 4 = 0, giving your answers to 1
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Select all that apply A The graph is a curve B3x 2y = 1 Plot families of exponential and reciprocal graphs For example y = 2 x, y = 3 x, y = 4 x y = 1÷x, y = 2÷x, y = 3÷x, Reduce a given linear equation in two variables to the standard form y = mx c; How to add a line to an existing Excel graph Adding a line to an existing graph requires a few more steps, therefore in many situations it would be much faster to create a new combo chart from scratch as explained above But if you've already invested quite a lot of time in designing you graph, you wouldn't want to do the same job twice
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Linearizing a graph means modifying the dependent and/or independent variables so that when you graph them, a straight line appears The simplest way to do this is to match the shape of your graph to one of several typical shapes that you would expect to see in a Physics class Appendix A displays the common types of graphs you Which graph shows the solution to the system of linear inequalities?X – 4y 4 y x 1 On a coordinate plane, 2 straight lines are shown The first solid line has a positive slope and goes through (0, negative 1) and (4, 0) Everything above the line is shaded The second dashed line has a positive slope and goes through (negative 1, 0) and (0
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10 Questions Show answers Question 1 SURVEY 300 seconds Q What is the gradient of the line y = 2x 3? The equation for this line is x=6 The meaning is that x will always be 6 since the line is straight, so it will stay on 6 and not cross any other axis Example 2 The line is a horizontal line We should look at the yintercept The equation is y=1 because the horizontal line will stay on one forever without crossing the xaxisUsing the equation of the line, in the form y = mx c Make sure you are familiar with the following topics before continuing Gradients of
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Explanation To graph a linear equation we need to find two points on the line and then draw a straight line through them Point 1 Let xHence the student should know that the graph of any first degree polynomial y =ax b is a straight line, and, conversely, any straight line has for its equation, y =ax b Sketching the graph of a first degree equation should be a basic skill See Lesson 33 of Algebra Example Mark the x and yintercepts, and sketch the graph of y = 2xSTRAIGHT LINE GRAPHS THE COORDINATES OF A POINT The coordinates of any point are written as an ordered pair (x, y) Point P in the diagram has coordinates (2, 3) Its horizontal distance along the x axis from the origin 0 is 2 units so the x coordinate is 2 Its vertical distance along the y axis from the origin is 3 units so the y
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