1. 3.1 Graphing Linear Equations
10/12/18

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

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

4. 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.

5. 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

6. 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

7. Determine if the equation in standard form.
½x = y – 5
6x – xy = 4
5x + y2 = 25
8 + y = 4x

8. 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 = 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.

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

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

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

12. 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

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