1. 3-1 Graphing Linear Equations
I can:
Determine whether an equation is linear.
Identify the x & y-intercepts from a graph.
Find x & y-intercepts from an equation.
Graph a linear equation using x & y-intercepts.
Identify x & y-intercepts from a table.
Graph a linear equation using a table.

2. Linear Function A functions whose graph forms a straight line.
Example 1: Determine whether each graph represents a function. If the graph does represent a function, is the function linear?

3. Linear Equation 𝐴𝑥+𝐵𝑦=𝐶, 𝑤ℎ𝑒𝑟𝑒 𝐴, 𝐵, 𝑎𝑛𝑑 𝐶, 𝑎𝑟𝑒 𝑟𝑒𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟𝑠
Any equation that can be
written in the standard form:
Standard Form of a Linear Equation
𝐴𝑥+𝐵𝑦=𝐶, 𝑤ℎ𝑒𝑟𝑒 𝐴, 𝐵, 𝑎𝑛𝑑 𝐶, 𝑎𝑟𝑒 𝑟𝑒𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟𝑠
𝑎𝑛𝑑 𝐴 𝑎𝑛𝑑 𝐵 𝑎𝑟𝑒 𝑛𝑜𝑡 𝑏𝑜𝑡ℎ 0.
NOTICE:
𝑥 & 𝑦 both have exponents of 1
𝑥 & 𝑦 are not multiplied together
𝑥 & 𝑦 do not appear in denominators, exponents, or radical signs.

4. Linear vs. Not Linear LINEAR Not LINEAR 3𝑥+2𝑦=10 3𝑥𝑦+𝑥=1 𝑦−2=3𝑥
𝑥 3 +𝑦=−1
−𝑦=5𝑥
𝑥+ 6 𝑦 =12

5. Example 2: Tell whether each graph is linear
Example 2: Tell whether each graph is linear. If it is, write it in standard form.
a) 𝑦=𝑥+3 b) 𝑦= 𝑥 2 c) 5𝑥=3𝑦−2 d) −3𝑥𝑦=5 e) 4𝑥+𝑦=−4𝑥+1

6. x-intercept
1) Where the line crosses the x-axis 2) 𝑦=0

7. y-intercept
1) Where the line crosses the y-axis 2) 𝑥=0

8. Why is standard form useful?
You can easily find the x & y intercepts and graph the line using those two points.

9. Example 3: Given the graph, state the x & y intercepts.b. c.
x-intercept:
y-intercept:
x-intercept:
y-intercept:
x-intercept:
y-intercept:

10. Example 4: 1) find the x& y intercepts 2) graph the line using the intercepts.

11. Example 4: 1) find the x& y intercepts 2) graph the line using the intercepts.
b. −9𝑥+6𝑦=−18

12. Example 4: 1) find the x& y intercepts 2) graph the line using the intercepts.

13. Example 4: 1) find the x& y intercepts 2) graph the line using the intercepts.

14. Example 5: Calculate the x & y intercepts for the following lines:

15. Example 5: Calculate the x & y intercepts for the following lines:
b) −8𝑥−10𝑦=−40

16. Example 5: Calculate the x & y intercepts for the following lines:

17. Example 6: The table shows the function relating the distance to an amusement park in miles and the time in hours the Torres family has driven. Find the x & y – intercepts and their meaning in this situation.

18. Example 7: Graph each equation by making an table.

19. Example 7: Graph each equation by making an equation.

20. Practice

21. Homework
Page : 1-10, 13-15, 21, 22, odd,