How to Convert Slope Form into Standard Form?
Last Updated : 11 Sep, 2024
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.
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 of a Line
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 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 the line in slope intercept form is:
y = mx + b
Where,
- m is Slope of Line
- b is y-intercept made by Line
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
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
Question 1: Write the equation 6x + 2y = 24 in slope-intercept form.
Solution:
Given:
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:
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:
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:
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:
Now, slope-intercept form
4x - 12y = -9
-12y = -(4x + 9)
12y = 4x + 9
y = (4/12)x + 9/12
y = 1/3x + 3/4
Similar Reads
How to Write a Whole Number in Standard Form? Identify the Whole Number: Writing a number in standard form starts with the whole number that one wants to convert. Place the Number in Decimal Form: A whole number in standard form means a number in decimal form which is normally depicted as an expanded form. For instance; if your whole number is
6 min read
How to Find the Slope of a Line From Its Graph Slope of a line is the measure of its inclination with the positive x-axis. Mathematically, the slope is defined as “rise over runâ€. The slope is the measure of the inclination or slant of the line, whether it is rising or falling. In this article, we will be discussing how to calculate the slope of
10 min read
Standard Form to Vertex Form - Quadratic Equation Quadratic equations are fundamental in algebra, often encountered in various forms. One common representation is the standard form and another useful form is the vertex form. Converting from standard form to vertex form allows for easier identification of the vertex and provides a clearer understand
8 min read
How to find the slope for a three-dimensional line? In three dimensions, lines don’t have a single slope like in 2D. Instead, use the direction vector, which shows the line’s direction. To find it:Identify two points on the line, say P(x_1, y_1, z_1) and Q(x_2, y_2, z_2).Calculate the direction vector: \vec{v} = (x_2 - x_1, y_2 - y_1, z_2 - z_1).This
3 min read
Point Slope Form Formula of a Line In geometry, there are several forms to represent the equation of a straight line on the two-dimensional coordinate plane. There can be infinite lines with a given slope, but when we specify that the line passes through a given point then we get a unique straight line. Different forms of equations o
6 min read