Standard Form
The standard form of a linear equation is Ax + By = C,
where A, B and C are real numbers, and A and B are not
both zero.
You can use the x-and y- intercepts to make a graph.
The x-intercept is the x-coordinate of the point where
a line crosses the x-axis. To graph a linear equation in
standard form, you can find the x-intercept by
substituting 0 for y and solving for x. Similarly, to find
the y-intercept, substitute 0 for x and solve for y.
Finding the x- and y-Intercepts
Find the x- and y- intercept of 3x + 4y = 8
Step 1: To find the x-intercept, substitute 0 for y and
solve for x.
Step 2: To find the y-intercept, substitute 0 for x and
solve for x.
If the x- and y-intercepts are integers, you can use
them to make a quick graph.
Graph Lines Using Intercepts
Example 2: Graph 2x + 3y = 12 using intercepts
Step 1: Find the intercepts.
Step 2: Plot and draw the points on the graph.
Graph Horizontal and Vertical Lines
A. Graph y = -3
Write in standard form.
___________________
B. Graph x = 2
Write in standard form.
__________________
Practice: Graph each equation.
1. y = 5
2. y = 0
3. x = -4
4. x = 0
You can change the equation from slope-intercept form
to standard form. If the equation contains fractions or
decimals, multiply to write the equation using integers.
Transforming to Standard Form
3
Example 4: Write y = 4 𝑥 + 2 in standard form using
integers.
Example 5: Real World Problem Solving
Data Analysis: Write an equation in standard form to
find the minutes someone who weighs 150 lbs. would
need to bicycle and swim laps in order to burn 300
calories. Use the data below.
Activity by a 150-lb person Calories Burned per Minute
Bicycling
Bowling
Hiking
Running 5.2 mi/h
Swimming laps
Walking 3.5 mi/h
10
4
7
11
12
5
Define: Let x = the minutes spent bicycling
Let y = the minutes spent swimming laps
Relate: 10 * minutes bicycling + 12 * minutes swimming
laps = 300 calories
Write: 10x + 12y = 300
The equation in standard form is 10x + 12y = 300
Practice: Write an equation in standard form to find
the minutes someone who weighs 150 lbs. would need to
bowl and walk to burn 250 calories.
Exercises: Find the x-and y-intercepts of each
equation.
1. x + 2y = 18
2. 3x – y = 9
3. -5x + y = 30
4. -6x + 3y = -9
5. 4x + 12y = -18
6. 9x – 6y = -72
7. -2x – 3y= -12
8. 7x – 2y = 4
Match the equation with its graph.
9. 2x – 5y = 10
11. 2x + 5y = 10
10. -2x + 5y = 10
Graph each equation using x- and y-intercepts.
12. x + y = 2
14. x – y = -7
13. x + y = -5
15. -3x + y = 6
16. -2x + y = -6
17. 5x – 3y = 15
For each equation, tell whether its graph is a horizontal
or a vertical line.
18. y = -1
19. x = 4
20. y = 2.5
21. x = - 3.75
Graph each equation.
22. y = 3
24. x = -7
25. y = -1.5
26. x = 4.5
Write each equation in standard form using integers.
27. y = 3x + 1
1
29. y = 2 𝑥 – 3
3
31. y = - 4 𝑥 – 4
33. y =
7
𝑥+
2
1
4
28. y = 4x – 7
2
30. y = = 3 𝑥 + 5
4
32. y = - 5 𝑥 – 7
2
34. y = - 5 𝑥 +
1
10
35. Fund Raising- The sophomore class holds a car
wash to raise money. A local merchant donates all of
the supplies. A wash costs $5 per car and $6.50 per
van or truck.
a. Define a variable for the number of cars. Devine a
different variable for the number of vans or trucks.
b. Write an equation in standard form to relate the
number of cars and vans or trucks the students must
wash to raise $800.
Graph each equation.
36. -3x + 2y = -6
37. x + y = 1
38. 2x – 3y = 18
39. y – x = -4