Graph Linear Systems Written in Standard Form

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Presentation transcript:

Graph Linear Systems Written in Standard Form

Types of Linear Equations Slope Intercept Form: y = mx + b You have used this one the most. If you have your slope and y-intercept, you can graph a line or even a system of equations (two lines). Standard Form: Ax + By = C “A” is the coefficient of “x.” “B” is the coefficient of “y.” “C” is a number (a constant)

What type of Equation is this? y = 2x -9 3x – 4y = 18 -x + 19y = 5 y = ½ x + 4 14x + y = 3 y = -2/3x – 9/2 Slope-Intercept Form Standard Form

Standard Form: Ax + By = C To graph an equation in standard form, you use the x- and y-intercepts. The x-intercept is: “What is x if y is zero?” (# , 0) The y-intercept is: “What is y if x is zero?” (0, #)

Find the x- and y- intercepts of the following equations: 4x + 2y = 12 3x – y = 6 -5x + 4y = 20 9x – 12y = -36 (3, 0) & (0, 6) (2, 0) & (0, -6) (-4, 0) & (0, 5) (-4, 0) & (0, 3)

It is where the two lines intersect. What does “Solving a Linear System” mean? It is where the two lines intersect.

Graph to solve the linear system. 2x – y = 2 4x + 3y = 24 Since the equations are in standard form, find the x- and y-intercepts to graph. 2x – y = 2 2x – 0 = 2 2x = 2 x = 1 (1, 0) 2(0) – y = 2 -y = 2 y = -2 (0, -2) 4x + 3y = 24 4x + 3(0) = 24 4x = 24 x = 6 (6, 0) 4(0) + 3y = 24 3y = 24 y = 8 (0, 8)

Graph to solve the linear system. 2x – y = 2 Intercepts are (1, 0) & (0, -2) 4x + 3y = 24 Intercepts are (6, 0) & (0, 8) Where do the lines intersect? (3, 4) is the solution to this system of linear equations.

Graph to solve the linear system. -4x – 2y = -12 4x + 8y = -24 Since the equations are in standard form, find the x- and y-intercepts to graph. -4x – 2y = -12 -4x – 2(0) = -12 -4x = -12 x = 3 (3, 0) -4(0) – 2y = -12 -2y = -12 y = 6 (0, 6) 4x + 8y = -24 4x + 8(0) = -24 4x = -24 x = -6 (-6, 0) 4(0) + 8y = -24 8y = -24 y = -3 (0, -3)

Graph to solve the linear system. -4x – 2y = -12 Intercepts are (3, 0) & (0, 6) 4x + 8y = -24 Intercepts are (-6, 0) & (0, -3) Where do the lines intersect? (6, -6) is the solution to this system of linear equations.