Solved Examples on Slope Intercept Form of a Line
Example 1: Find the equation of the straight line passing through (3, 3) and that has slope m = 5.
Solution:
Given,
Coordinates at which the line passes are (3, 3)
Slope of the line (m) = 5
The slope-intercept form of the line is,
y = mx+c
Substituting the values of (x, y) and m to get the value of c.
3 = 5(3) + c
⇒ 3 = 15 + c
⇒ c = 3 – 15 = -12
Thus, the required equation is,
y = 5x – 12
Example 2: Find the equation of the straight line passing through (0, 0) and that has slope m = 1/3.
Solution:
Given, Coordinates at which the line passes are (0, 0)
Slope of the line (m) = 1/3
The slope-intercept form of the line is,
y = mx+c
Substituting the values of (x, y) and m to get the value of c.
0 = 1/3(0) + c
⇒ c = 0
Thus, the required equation is,
y = (1/3)x + 0
⇒ 3y = x
Example 3: Find the equation of the lines if m = 1 and,
- y-intercept made by line (c) is 4
- x-intercept made by line (d) is 7
Solution:
Given: m = 1
(i) y-intercept = c = 4
Equation of the line in slope-intercept form is,
y = mx + c
⇒ y = (1)x + (4)
⇒ y = x + 4
⇒ x – y + 4 = 0
This is the required equation.
(ii) x-intercept = d = 7/3
Equation of line if slope and x-intercept given is,
y = m(x – d)
⇒ y = (1)[x – 7]
⇒ y = x – 7
⇒ x – y – 7 = 0
This is the required equation.
Example 4: Find the equation of the line in standard form if the slope-intercept form of the line is y = 2/3(x) + 7/9.
Solution:
Given equation,
y = 2/3(x) + 7/9
Standard form of the equation is ax + by + c = 0
Now given the equation in slope-intercept form,
y = 2/3(x) + 7/9
Simplifying,
⇒ y = 6/9(x) + 7/9
⇒ y = (6x + 7)/9
⇒ 9y = 6x + 7
⇒ 6x + (-9)y + 7 = 0
This is the required equation in standard form and a = 6, b = -9, and c = 7.
Slope Intercept Form
Slope Intercept Form of a line is one of the many standard forms of equation of line. Equation of line is the algebraic way to represent a line.The various ways of representing the equation of a straight line are,
- Slope intercept form
- Intercept form
- Point slope form
- Two point form
Slope intercept form of the equation is used to represent the equation of a straight line when the slope of the equation and the intercept on the y-axis is given.
In this article, we will learn about the slope-intercept form of a straight line, its derivation, graphs, and examples.
Table of Content
- What is Slope Intercept Form of a Line?
- General Equation of Slope Intercept Form
- How to Derive the Slope Intercept Form?
- Derivation from Point-Slope Form
- Derivation from Two Point Form
- Other Equation Related to Slope Intercept Form
- Slope Intercept Form (When x Intercept is given)
- Slope Intercept Form of Line Passing Through Origin
- Slope Intercept Form Graph
- FAQs on Slope Intercept Form