find the equation of the line whose slope=2 and intercept=-4
Answers
Given : A straight line has a slope of 2 and has an intercept of 4.
To find : The equation of the line.
Solution:-
In the question we are not specified wheather -4 is x intercept or y intercept. Let's solve for both the cases.
If y intercept is given:
The equation of a straight line whose slope and y intercept is given, is given by:
- y = mx + c
Here m is the slope of the line and c is y intercept.
For our question, m = 2 and c = -4
⇒ y = mx + c
⇒ y = 2x + (-4)
⇒ y = 2x - 4
⇒ 2x - y - 4 = 0
This is the required equation.
If x intercept is given:
The equation of a straight line whose slope and x intercept is given, is given by:
- y = m(x - d)
Here m is the slope and d is x intercept.
For our question, m = 2 and d = -4
⇒ y = m(x - d)
⇒ y = 2(x - (-4))
⇒ y = 2(x + 4)
⇒ y = 2x + 8
⇒ 2x - y + 8 = 0
This is the required equation.
Additional Information:
Slope is the measure of the steepness of a line. It gives the direction of a line with positive x axis.
Slope is obtained by tan(θ) where θ is the inclination of the line with positive x axis measured anti-clockwise.
Slope is generally denoted by m.
When 2 points through which the line passes are given, then slope of a line is given by:
- m = (y2 - y1)/(x2 - x1)
Given the condition that the line passes from (x1, y1) and (x2, y2).