Question

Q1. Transform the equation √3x + y = 4 into (a) slope - intercept form (b) Intercept form
and (c) normal form​

Answer 1

Step-by-step explanation:

Given Equation : √3x + y = 4

a) Slope - intercept form

General form : y = mx + c.

For the given equation :

$</p><p>\begin{gathered} \sqrt{3} x + y = 4 \\ \\ y = - \sqrt{3} x + 4\end{gathered} </p><p>$

b) Intercept form

General form : x/a + y/b = 1

For the given equation :

$</p><p>\begin{gathered} \sqrt{3} x + y = 4 \\ \\ \frac{ \sqrt{3} }{4} x + \frac{1}{4}y = 1 \\ \\ \frac{x}{( \frac{4}{ \sqrt{3} }) } + \frac{y}{4} = 1\end{gathered}$

c) Normal form

General form : xcosθ + y sinθ= p

For the given equation,

$\begin{gathered} \sqrt{3} x + y = 4 \\ \\ \frac{ \sqrt{3}x + y }{2} = \frac{4}{2} \\ \\ \frac{ \sqrt{3} }{2} x + \frac{1}{2} y = 2\end{gathered}$

where, cosθ = √3/2, sinθ = 1/2