3.1 Graphing Linear Equations 10/12/18

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 Rules in order to be in Standard Form The x and y must not have exponents : x2 + y = 4 The x and y must not be multiplied: xy – 4y = 2 The x value must not be negative or a fraction: - 2x + y = 9 Or 1/2x + 4y = 7 The x and y value must be on one side of the equation and the constant( c ) on the other side. Ax + By = c 5x – 3y = 2 x + 4 = 6 4 + y = 5

Determine if the equation in standard form. ½x = 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 three points then draw a line through them. X Y = 3x Y XY -2 - 1 1 2

Determine whether each equation is a linear equation. Write yes or no. 1. 2x = 4y 2. 6 + y = 8 3. 4x – 2y = - 1 4. 3xy + 8 = 4y 5. 3x – 4 = 12 6. y = x2 + 7