1. Lesson 6-3 (Part 1) Standard Form page 298
Objective: To graph equations using intercepts.

2. Real-World Connection
We can use an equation to model a situation that involves exercise, as in example 5.

3. where A, B, and C are real numbers and
DEFINITION
Standard form of a linear equation:
Ax + By = C
where A, B, and C are real numbers and
A and B are not zero.
x-intercept—the x-coordinate of the point where a line crosses the x-axis
y-intercept– the y-coordinate of the point where a
line crosses the y-axis

4. Standard Form Find the x- and y-intercepts of 2x + 5y = 6.
ALGEBRA 1 LESSON 6-3
Find the x- and y-intercepts of 2x + 5y = 6.
Step 2  To find the y-intercept,
substitute 0 for x and
solve for y.
2x + 5y = 6
2(0) + 5y = 6
5y = 6
y =
The y-intercept is . 6 5
Step 1  To find the x-intercept, substitute 0 for y and
solve for x.
2x + 5y = x + 5(0) = x = x = 3
The x-intercept is 3.
6-3

5. Example 1, page 299
Find the x and y intercept of
3x + 4y = 8.

6. Example 1, page 299
Find the x-and y-intercepts of
4x – 9y = -12.

7. Graphing Using Intercepts
Find the x-intercept by substituting zeros for y.
Find the y-intercept by substituting zeros for x.
Plot the intercepts.
Draw the line.

8. Standard Form Graph 3x + 5y = 15 using intercepts.
ALGEBRA 1 LESSON 6-3
Graph 3x + 5y = 15 using intercepts.
Step 1  Find the intercepts.
3x + 5y = 15
3x + 5(0) = 15 Substitute 0 for y.
3x = 15 Solve for x.
x = 5
3(0) + 5y = 15 Substitute 0 for x.
5y = 15 Solve for y.
y = 3
Step 2  Plot (5, 0) and (0, 3).
Draw a line through the points.
6-3

9. Example 2, page 299 Graph 2x + 3y = 12 using the x- and y-intercepts.5 -5

10. Example 2, page 299 Graph 5x + 2y = -10 using the x- and y-intercepts.-5

11. either A or B = 0, but not both.
Special Lines
In standard form
Ax + By = C
either A or B = 0, but not both.
If A = 0, the line is horizontal and the equation looks like: y = #.
If B = 0, the line is vertical and the equation looks like: x = #.

12. Standard Form a. Graph y = 4 b. Graph x = –3.
ALGEBRA 1 LESSON 6-3
a. Graph y = 4
b. Graph x = –3.
0 • x + 1 • y = 4 Write in standard form.
For all values of x, y = 4.
1 • x + 0 • y = –3 Write in standard form.
For all values of y, x = –3.
6-3

13. Example 3, page 299 Graph each equation.
a) y = b) x = 2 y x 5 -5 y x 5 -5

14. Example 3, page 299 Graph each equation.
a) y = 5 b) y = 0 y x 5 -5 y x 5 -5

15. Example 3, page 299 Graph each equation.
c) x = -4 d) x = 0 y x 5 -5 y x 5 -5

16. Summary
What did you learn today?

17. SUMMARY Standard form of an equation is Ax + By = C
A horizontal line has equation y = #.
A vertical line has equation x = #.

18. ASSIGNMENT
Lesson 6-3 page 301
#1-26 all, all