Equation of the line is represented in various forms such as standard form, slope-intercept form and others, one can easily convert the slope-intercept form of a line to standard form.
In this article, we have covered How to Convert the Slope Form of a Line into the Standard Form of a Line and related examples in detail.
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What is Slope of a Line?
Slope of a line is a measure of its steepness or incline, defined as the ratio of the vertical change between two points on the line to the horizontal change between the same two points. It indicates how much the line rises or falls for every unit of horizontal distance travelled. It is denoted using the letter 'm'.
Slope is the rate of change of y with respect to x. It simply means the slope is the rate of change of one given variable with respect to the other.
Equation of Line in Standard form
Equation of the line in standard form is:
ax + by + c = 0
Where,
a, b, and c are constant and a, and b are never zero.
Equation of Line in Slope-Intercept Form
Equation of the line in slope intercept form is:
y = mx + b
Where,
- m is Slope of Line
- b is y-intercept made by Line
Converting From Slope-Intercept to Standard Form
Standard form of a line is given by
Ax + By = C
Where, A, B, and C are constants.
As mentioned above, find the slope of a line by putting the linear equation in slope-intercept form and then, So,
- Subtracting Ax from both sides of the equation
Ax - Ax + By = C - Ax
By = -Ax + C
- Dividing both sides by B
By/B = -Ax/B + C/B
y = -Ax + C/B
y = (-A/B)x + (C/B)
Now, the slope of a line, in general, can be determined by the given formula.
m = -A/B
Sample Questions on Converting From Slope-Intercept to Standard Form
Question 1: Write the equation 6x + 2y = 24 in slope-intercept form.
Solution:
Given:
- 6x + 2y = 24
Now, slope-intercept form
6x + 2y = 24
2y = -6x + 24
y = (-6/2)x + (24/2)
y = -3x + 12
Question 2: Put the following linear equation -3x + y = 4 in slope-intercept form.
Solution:
Given:
- -3x + y = 4
Now, slope-intercept form
-3x + y = 4
y = 3x + 4
Question 3: Put the following standard equation 2x + 3y = 15 in slope-intercept form.
Solution:
Given:
- 2x + 3y = 15
Now, slope-intercept form
2x + 3y = 15
3y = -2x + 15
y = (-2/3)x + 5
Question 4: Put the following standard equation 2y - 8x = -24 in slope-intercept form.
Solution:
Given:
- 2y - 8x = -24
Now, slope-intercept form
2y = 8x - 24
y = (8/2)x - 24/2
y = 4x - 12
Question 5: Put the following standard equation 4x - 12y = -9 in slope-intercept form.
Solution:
Given:
- 4x - 12y = -9
Now, slope-intercept form
4x - 12y = -9
-12y = -(4x + 9)
12y = 4x + 9
y = (4/12)x + 9/12
y = 1/3x + 3/4