1. Graphing Linear Equations in Standard Form
3.4
Graphing Linear Equations in Standard Form
How can you describe the graph of the equation 𝐴𝑥+𝐵𝑦=𝐶?
Students will be able to graph equations of horizontal and vertical lines.
Students will be able to use graph equations in standard form using intercepts.

2. Students will be able to graph equations of horizontal and vertical lines.
The standard form of a linear equation is 𝐴𝑥+𝐵𝑦=𝐶, where A, B, and C are integers (no fractions) and have no common factors.
If 𝐴=0, then the equation is 𝐵𝑦=𝐶, or 𝑦= 𝐶 𝐵 .
Since 𝐶 𝐵 is a constant we can write 𝑦= 𝐶 𝐵 , as 𝑦=𝑏.
Similarly
If 𝐵=0, then the equation is 𝐴𝑥=𝐶, or 𝑥= 𝐶 𝐴 .
Since 𝐶 𝐴 is a constant we can write 𝑥= 𝐶 𝐴 , as 𝑥=𝑎.

3. Students will be able to graph equations of horizontal and vertical lines.
What kind of line is this?
Horizontal
What are the coordinates of these points?
What do all these coordinates have in common?
The same y-coordinate, therefore, the equation of this line is 𝑦=2.
The graph of 𝑦=𝑏 is a horizontal line.
The line passes through the point (0,𝑏).

4. Students will be able to graph equations of horizontal and vertical lines.
What kind of line is this?
Vertical
What are the coordinates of these points?
What do all these coordinates have in common?
The same x-coordinate, therefore, the equation of this line is 𝑥=−3.
The graph of 𝑥=𝑎 is a vertical line.
The line passes through the point (𝑎,0).

5. Students will be able to graph equations of horizontal and vertical lines.
What is the equation of the following lines?
𝑦=−3
𝑥=4
Where do the two lines intersect?
(4,−3)

6. You Try!!!
Students will be able to graph equations of horizontal and vertical lines.
What is the equation of the following lines?
𝑥=−1
𝑦=4
Where do the two lines intersect?
(−1,4)

7. 2. Students will be able to use graph equations in standard form using intercepts.
The x-intercept of a graph is the x-coordinate of a point where the graph crosses the x-axis.
It occurs when 𝑦=0
The y-intercept of a graph is the y-coordinate of a point where the graph crosses the y-axis.
It occurs when 𝑥=0
y-intercept = b
(0,b)
x-intercept = a
(a,0)

8. Now plot the points and draw the line.
2. Students will be able to use graph equations in standard form using intercepts.
To graph the linear equation 𝐴𝑥+𝐵𝑦=𝐶, find the intercepts and draw the line that passes through the two intercepts.
To find the x-intercept, let 𝑦=0 and solve for x.
To find the y-intercept, let 𝑥=0 and solve for y.
Use intercepts to graph the equation 3𝑥+4𝑦=12.
To find the x-intercept, let 𝑦=0 and solve for x.
3𝑥+4(0)=12
3𝑥=12
𝑥=4
x-intercept is (4,0)
To find the y-intercept, let 𝑥=0 and solve for y.
3(0)+4𝑦=12
4𝑦=12
𝑦=3
y-intercept is (0,3)
Now plot the points and draw the line.

9. 2. Students will be able to use graph equations in standard form using intercepts.
Use intercepts to graph the equation 3𝑥+4𝑦=12.
To find the x-intercept, let 𝑦=0 and solve for x.
3𝑥+4(0)=12
3𝑥=12
𝑥=4
x-intercept is (4,0)
To find the y-intercept, let 𝑥=0 and solve for y.
3(0)+4𝑦=12
4𝑦=12
𝑦=3
y-intercept is (0,3)

10. 2. Students will be able to use graph equations in standard form using intercepts.
Use intercepts to graph the equation 2𝑥−𝑦=4.
To find the x-intercept, let 𝑦=0 and solve for x.
2𝑥−(0)=4
2𝑥=4
𝑥=2
x-intercept is (2,0)
To find the y-intercept, let 𝑥=0 and solve for y.
2 0 −𝑦=4
−𝑦=4
𝑦=−4
y-intercept is (0,-4)

11. You Try!!
2. Students will be able to use graph equations in standard form using intercepts.
Use intercepts to graph the equation 𝑥+3𝑦=−9.
𝑥+3 0 =−9
𝑥=−9
x-intercept is (-9,0)
0 +3𝑦=−9
3𝑦=−9
𝑦=−3
y-intercept is (0,-3)

12. So let’s review!
What have we covered so far?
Students will be able to graph equations of horizontal and vertical lines.
Horizontal lines are 𝑦=𝑏
Vertical lines are 𝑥=𝑎
2. Students will be able to use graph equations in standard form using intercepts.
To find the x-intercept, 𝑦=0, and solve for x.
To find the y-intercept, 𝑥=0, and solve for y.