3.1 Graphing Linear Equations 10/10/16

CC State Standards For a function that models a relationship between two quantities , interpret key features of graphs and tables.

New Vocabulary Linear equation Standard Form Constant X – axis Y - axis X – Intercept Y - Intercept

Definitions Linear equations – An equation that forms a line when it is graphed. Standard form – The standard form of a linear equation is Ax + By = C. Constant – In a linear equation, C is called a constant, or a real number. Ax and By are variable terms.

Definitions X – Axis – The horizontal number line on a coordinate plane. Y – Axis – The vertical number line on a coordinate plane. X – Intercept –The x-coordinate of the point at which the graph of an equation crosses the x – axis. Y – Intercept – The y-coordinate of the point at which the graph crosses the y-axis

Standard Form of a Linear Equation Ax + By = C IE. 3x + y = 4 A = 3 , B = 1 , C = 4. This is a linear equation because it is written in standard form Determine whether each equation is a linear equation. Write the equation in standard form. x = y – 5 6x – xy = 4 5x + y2 = 25 8 + y = 4x

Graph each equation by using the X and Y intercepts y = 4 + x To find the x-intercept, let y = 0. 0 = 4 + x then isolate the variable -4 -4 -4 = x This means the graph intersects the x-axis at (-4,0) To find the y intercept, let x = 0. y = 4 + 0 y = 4 This means the graph intersects the y-axis at (0,4). Plot these points then draw a line through them.

Graph each equation by using the X and Y intercepts 2x – 5y = 1 y = 4 + 2x

Graph each equation by making a table. Y = 2x (X,Y) -2 -1 1

Graph each equation by making a table. 6x – 3y = - 3 Get “y” by itself -2 -1 1

TOTD Graph each equation by making a table. Y = 3x Plot the two points then draw a line through them. X Y = 3x Y XY -2 - 1 1 2