Example y = 2x 1 is a linear equation The graph of y = 2x1 is a straight line When x increases, y increases twice as fast, so we need 2x; NCERT Exemplar Class 9 Maths Chapter 4 Exercise 44 Question 1 Show that the points A (1, 2), B (1, 16) and C (0, – 7) lie on the graph of the linear equation y = 9x – 7 Solution Firstly, to draw the graph of equation y = 9x – 7, we need atleast two solutions When x = 2, then y = 9 (2) – 7 = 18 – 7 = 11Linear functions commonly arise from practical problems involving variables , with a linear relationship, that is, obeying a linear equation =If , one can solve this equation for y, obtaining = = , where we denote = and =That is, one may consider y as a dependent variable (output) obtained from the independent variable (input) x via a linear function = =
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Is y=x^3-4 a linear equation
Is y=x^3-4 a linear equation- Solve the system by graphing \(\left\{ \begin{array} {l} y = \tfrac{1}{2}x4 \\ 2x4y = 16 \end{array}\right \) Answer infinitely many solutionsAnother common way to write linear equations is as (y q) = a(xL p), where a;p;q2R are constants This is called the pointslope form of a linear equation Examples include (y 2) = 7(x 3) and (y 1) = 2(x 4) Claim Let L R 2be the line containing the point (p;q) 2R and having slope equal to the number a Then (y q) = a(x p) is an equation for L
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Solve the following systems of equations 4/x 5y = 7 3/x 4y = 5 asked Apr 26 in Linear Equations by Haifa (k points) pair of linear equations in two variables;X y = 14x y = 4 the equation have unique solutionPair of linear equations are consistentStep by step guide to writing linear equations The equation of a line in slope intercept form is y = mx b y = m x b Identify the slope Find the y y –intercept This can be done by substituting the slope and the coordinates of a point (x,y) ( x, y) on the line Writing Linear Equations
System of Linear Equations entered 1 y=x4 2 y4=x Equations Simplified or Rearranged 1 y x= 4 2 y x= 4 Solve by Substitution // Solve equation 2 for the variable y 2 y = x 4When x is 0, y is already 1 So 1 is also needed; So we know that the first number is the xaxis (2) and the second one the yaxis (6) and the linear equation is y= x4 let's plug in the numbers 6=24 Wait does that make sense to you The answer is A (1,5) y=x4 5= 14 Hope it make and that was a fake mssue 👍
So, the equation is y = \(\frac { 1 }{ 4 } \)x 9 The linear function is g(x) = \(\frac { 1 }{ 4 } \)x 9 Monitoring Progress Question 7 The corresponding data for electricity generated by hydropower are 248 million megawatt hours in 07 and 277 million megawatt hours in 12The given linear equation is 2x−y = 4 2x−y = 4 Put y = 0 ⇒ 2x−0 = 4 ⇒ 2x =4Linear equations A linear equation is an equation that represents a straight line When plotted on a graph, a linear equation always results in a straight line, as in the figure below, which is a special case of a linear equation referred to as the identity function, y = x
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Each solution (x, y) of a linear equation = may be viewed as the Cartesian coordinates of a point in the Euclidean planeWith this interpretation, all solutions of the equation form a line, provided that a and b are not both zero Conversely, every line is the set of all solutions of a linear equation The general equation for that form is y = mx b where m is the slope and b is the yintercept So we'll get x y = 4 y = − x 4 The yintercept is 4, so that's a point (0,4) The slope is −1, so the graph will move one point down for every point itX 5y = 4
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Xy=4 This question is from textbook Answer by Alwayscheerful (414) ( Show Source ) You can put this solution on YOUR website! Students can also refer to NCERT Solutions for Class 9 Maths Chapter 4 Linear Equations for Two Variables for better exam preparation and score more marks Linear Equations for Two Variables Class 9 MCQs Questions with Answers Question 1 The value of y at x = 1 in the equation 5y = 2 is (a) \(\frac{5}{2}\) (b) \(\frac{2}{5}\) (c) 10 (d) 0 Most linear equations that you will encounter are conditional and have one solution If solving a linear equation leads to a true statement like \(0 = 0\), then the equation is an identity and the solution set consists of all real numbers, \(R\)
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The easiest way to graph a line is in slopeintercept form multiply by 1 because y must be positive your slope of the line is 1A 5/6 b 3/6X−y = 14 xy = 4 2x = 18 x = 9,y = 4−x = 4−9= −5∴ x= 9,y = −5
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Solve the Following Simultaneous Equation5x 2y = –3;Let S be the set of all λ ∈R for which the system of linear equations 2x – y 2z = 2 x–2y λz = –4 x λy z = 4 has no solution Then the set S (1) contains more than two elements (2) is a singleton (3) contains exactly two elements (4) is an empty setFinding a Linear Equation Perhaps the most familiar form of a linear equation is the slopeintercept form, written as y = m x b \displaystyle y=mxb y = mx b, where m = s l o p e \displaystyle m=\text {slope} m = slope and b = y i n t e r c e p t \displaystyle b=y\text {intercept} b = yintercept Let us begin with the slope
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