1. Graphing Linear Equations
By Using Intercepts

2. Before we begin graphing, let’s review writing equations in standard form, ax + by = c.
Example 1: Rewrite the equations in standard form.
a) 3x + 4 = 2y b) 5(x – 3) = 2y
5y – 4x = 20 d) ½x + ¾y = 1
3x – 2y = – 4
5x – 2y = 15
–4x + 5y = 20
2x + 3y = 4

3. An equation for which the graph is a line
Linear Equation
An equation for which the graph is a line

4. Any ordered pair of numbers that makes a linear equation true.
Solution
Any ordered pair of numbers that makes a linear equation true.

5. .(0 , 5 ) .(2 , 0) 5x + 2y = 10 This is the graph of 5x + 2y = 10
Notice that the graph intersect the axes.
At what point does the graph intersects the x-axis? At what point does the graph intersects the y-axis?
The x-intercept of a line is the x-coordinate of a point where the line intersects the x-axis. While the y-intercept of a line is the y-coordinate of a point where the line intersects the y-axis.
Does the x-intercept of a line is 2 and y-intercept of a line is 5

6. Where the line crosses the x-axis
X-intercept
Where the line crosses the x-axis

7. The x-intercept has a y coordinate of ZERO

8. To find the x-intercept, plug in ZERO for y and solve

9. Where the line crosses the y-axis
Y-intercept
Where the line crosses the y-axis

10. The y-intercept has an x-coordinate of ZERO

11. To find the y-intercept, plug in ZERO for x and solve

12. Graph -2x + 3y = 12 Find your x-intercept: Let y = 0 -2x + 3y = 12
x = -6; (-6, 0)
Find your y-intercept:
Let x = 0
-2(0) + 3y = 12
3y = 12
y = 4; (0, 4)
Graph -2x + 3y = 12
3. Graph both points and draw a line through them.

13. Graph 4x – 8 = –y 4x + y = 8 Find your x-intercept: Let y = 0
x = 2; (2, 0)
Find your y-intercept:
Let x = 0
0 + y = 8
y = 8
y = 8; (0, 8)
Graph 4x – 8 = –y
3. Graph both points and draw a line through them.

14. Graph 3y – 15 = 2x -2x + 3y = 15 Find your x-intercept: Let y = 0
x = -15/2; (-15/2, 0)
Find your y-intercept:
Let x = 0
-2(0) + 3y = 15
3y = 15
y = 5; (0, 5)
Graph 3y – 15 = 2x
3. Graph both points and draw a line through them.

15. Graph 2x – 10 = – 5y 2x = 10 2 2 x = 5; (5, 0) 5y = 10 5 5 y = 2
1.Find your x-intercept:
Hide the variable y
2x = 10
x = 5; (5, 0)
2. Find your y-intercept:
Hide the variable x
5y = 10
5 5
y = 2
y = 2; (0, 2)
Graph 2x – 10 = – 5y
3. Graph both points and draw a line through them.

16. Graph – 5y = 2x + 20 -2x = 20 -2 -2 x = -10; (-10, 0) -5y = 20 -5 -5
1.Find your x-intercept:
Hide the variable y
-2x = 20
x = -10; (-10, 0)
2. Find your y-intercept:
Hide the variable x
-5y = 20
-5 -5
y = -4
y = -4; (0, -4)
Graph – 5y = 2x + 20
3. Graph both points and draw a line through them.

17. Determine the x- and y-int. of the ff.
x-int.
y-int. 1
3x + y = 3 ___ ___
2x + 5y = 10 ___ ___
4x – 6y = 12 ___ ___
6x = 2y – 4 ___ ___
x = 2y ___ ___ 3 2 5 3 -2 2
-2/3 7
-7/2

18. Determine the x- and y-int. of the ff. 2x + y = 4 ___ ___
Seatwork:
Determine the x- and y-int. of the ff.
2x + y = 4 ___ ___
x – y = 5 ___ ___
y = –x + 3 ___ ___
y = 2x + 3 ___ ___
x = y – 6 ___ ___
B. Graph nos. 4 and 5
x-int.
y-int.