Linear equations are “straight line” equations have simple variable expressions with terms without exponents on them. You are dealing with straight line equation, if you come across an equation with only x and y. To find the equation of a line and y-intercept in the steepness of the line, we use slope intercept form formula.
Formula for Point Slope-Intercept Form
The point slope formula is given as:
| y = mx + b |
The values used in formula are as follows:
- m is the slope of the line
- b is the y-intercept of the line
Solved Examples
Question 1: With the slope 6 and y-intercept 4, find the equation of a line?
Solution:
Here,
m = 6 and
b = 4
With the formula: y = mx + b
The equation of the line will be y = 6x + 4
Question 2: Write the equation of the line in slope-intercept form where slope is -2 and passing through the point (0, 9).
Solution:
Given,
Slope = m = -2
Point = (x, y) = (0, 9)
Equation of a line in slope-intercept form is:
y = mx + b….(i)
According to the given,
9 = (-2)(0) + b
b = 9
Substituting the value of m and b in equation (i),
y = -2x + 9
This is the required equation of a line in slope-intercept form.
Question 3: Find the slope and y-intercept of the equation of line 2x – y + 5 = 0.
Solution:
Given equation of a line:
2x – y + 5 = 0
Thus,
y = 2x + 5
This is of the form y = mx + b
Here, m = 2 and b = 5
Therefore, slope = 2 and y-intercept = 5
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