Applied Algebra B Lesson 6 3 Graphing Linear

Applied Algebra B Lesson: 6 – 3 Graphing Linear Relationships Objective: Learn to graph linear relations.

Linear Equation is an equation whose graph is a straight line. Can be written in Standard form Ax + By = C A, B, & C are integers A & B are both not 0 A is greater than or equal to 0 A, B, & C have a common factor of 1

Linear vs. Nonlinear Linear Equations 3 x + 4 y = 6 y = -2 8 b = -2 a - 5 Nonlinear Equations 2 x + 4 y = 3 z 2 2 x + 2 xy = 3 2 x 2 = 7

Determine whether each equation is a linear equation. Explain. If an equation is linear, identify A, B, and C when written in standard form. 3 x = 5 + y First write in Ax + By = C form 3 x = 5 + y -y -y 3 x – y = 5 A = 3, B = -1, C = 5 Does it meet all requirements? A, B, & C are integers A & B are both not 0 A is greater than or equal to 0 A, B, & C have a common factor of 1 Yes so the equation is linear.

Determine whether each equation is a linear equation. Explain. If an equation is linear, identify A, B, and C when written in standard form. -2 x + 3 xy = 6 First write in Ax + By = C form Can’t write in Ax + By = C form since x and y are being multiplied. . Not a linear equation.

Determine whether each equation is a linear equation. Explain. If an equation is linear, identify A, B, and C when written in standard form. x = -2 First write in Ax + By = C form x = -2 is a simplified version of 1 x + 0 y = -2 x = -2 A = 1, B = 0, C = -2

Determine whether each equation is a linear equation. Explain. If an equation is linear, identify A, B, and C when written in standard form. 8 + y = 2 x First write in Ax + By = C form 8 = 2 x – y Same as 2 x – y = 8 A = 2, B = -1, C = 8

Determine whether each equation is a linear equation. Explain. If an equation is linear, identify A, B, and C when written in standard form. -5 z = 4 x + 2 y First write in Ax + By = C form Not linear because there are 3 different variables. What if -5 x = 4 x + 2 y? 0 = 9 x + 2 y is linear.

Determine whether each equation is a linear equation. Explain. If an equation is linear, identify A, B, and C when written in standard form. y 2 = 4 First write in Ax + By = C form Not linear since there is an exponent. What about y = 4? y = 4 is linear.

Graph the equation. Book went by 2’s y = 2 x - 3 I would go by 1’s. Make a t-chart. You can pick any x’s you want. Pick at least 3. x y 0 -3 1 -1 2 1 Draw the line so that It touches at least 2 quadrants.

Graph the equation. 2 x + 4 y = 8 Solve for y first. x y 0 2 2 1 4 0

Graph the equation. Describe the graph. y=3 Do we know what x is? Pick any x, what is y? x y 0 3 1 3 2 3 Horizontal line at 3 *Hint* When there is only 1 variable, the line will go through the axis that the equation gives you. y = 3 goes through y-axis.

Graph the equation. Describe the graph. x = -2 Do we know what y is? Pick any y, what is x? x y -2 0 -2 1 -2 3

Homework Pg. 254 1 – 12 all, 14 – 42 EOE