What is the Standard form of a line? It is a way to write the equation of a line that is defined by Ax + By = C, where A,B, and C are real numbers and A and B are not zero.
How to use the Standard Form of a Line:
We can use the standard form of a line to quickly understand the x and y intercepts of the line.
For example, the line 2x + 3y = 12
If we set x=0, then 3y = 12 and y = 4. So the y intercept is (0,4)
If we set y=0, then 2x = 12 and x = 6. So the x intercept is (6,0)
We can also convert the slope-intercept form of a line into the standard form.
For example y= 3/8(x) + 5
First, put all variables on one side:
y – 3/8(x) = 5
Then, multiply the entire equation by the denominator
8y – 3x = 40 or -3x +8y = 40
Sample Math Problems
Question
What is the x intercept of 5x + 3y = 15
Solution
To find the x intercept, set y=0.
When y=0, 5x=15 and x = 3. Therefore, the x intercept is (3,0)
Question
What is the y intercept of 5x + 3y = 15
Solution
To find the y intercept, set x=0.
When x=0, 3y = 15 and y = 5. Therefore, the x intercept is (0,5)
Question
What is y = -2x + 2/7 in standard form?
Solution
y + 2x = 2/7
7 (y + 2x = 2/7)
7y + 14x = 2 or 14x + 7y = 2
Question
What is y = 2/3(x) + 5 in standard form?
Solution
y – 2/3x = 5
3(y – 2/3x = 5)
3y – 2x = 15
