A straight line, L, is perpendicular to the line with the equation y=2x+3
L passes through the point (10,3)
Find the equation for the straight line L (4 marks)
Answers
EXPLANATION.
A straight line L , is perpendicular to the line with the equation y = 2x + 3.
Passes through the point = (10,3).
As we know that,
Slope of perpendicular line : ax + by + c = b/a.
Slope of perpendicular line : 2x - y + 3 = -1/2.
Equation of the straight line.
⇒ (y - y₁) = m(x - x₁).
Put the value in the equation, we get.
⇒ (y - 3) = -1/2(x - 10).
⇒ 2(y - 3) = -1(x - 10).
⇒ 2y - 6 = - x + 10.
⇒ 2y - 6 + x - 10 = 0.
⇒ 2y + x - 16 = 0.
⇒ x + 2y = 16.
∴ The equation of line is x + 2y = 16.
MORE INFORMATION.
Different forms of the equation of straight line.
(1) Slope - Intercept form : y = mx + c.
(2) Slope point form : The equation of a line with slope m and passing through a point (x₁, y₁) is : (y - y₁) = m(x - x₁).
(3) Two point form : (y - y₁) = [(y₂ - y₁)/(x₂ - x₁)](x - x₁).
(4) Intercept form : x/a + y/b = 1.
(5) Normal (perpendicular) form of line : x cosα + y sinα = p.
(6) Parametric form (distance form) : (x - x₁)/cosθ = (y - y₁)/sinθ = r.