Question

13. Transform the equation x+y- 2 = 0) into slope intercept form, intercept form and
Normal form​

Answer 1

$\underline{\textsf{Given:}}$

$\textsf{Line is x+y-2=0}$

$\underline{\textsf{To find:}}$

$\textsf{Slope intercept form, Intercept form and Normal form of the line}$

$\underline{\textsf{Solution:}}$

$\underline{\textsf{Slope intercept form:}}$

$\mathsf{x+y-2=0}$

$\textsf{This can be written as}$

$\mathsf{y=-x+2}$

$\textsf{This equation is of the form y=mx+c}$

$\underline{\textsf{Intercept form:}}$

$\mathsf{x+y-2=0}$

$\textsf{This can be written as}$

$\mathsf{x+y=2}$

$\textsf{Divide bothsides by 2}$

$\mathsf{\dfrac{x}{2}+\dfrac{y}{2}=1}$

$\textsf{This equation is of the form}\;\mathsf{\dfrac{x}{a}+\dfrac{y}{b}=1}$

$\underline{\textsf{Normal form:}}$

$\mathsf{x+y-2=0}$

$\textsf{This can be written as}$

$\mathsf{x+y=2}$

$\textsf{Divide bothsides by}\;\mathsf{\sqrt{2}}$

$\mathsf{\dfrac{x}{\sqrt{2}}+\dfrac{y}{\sqrt{2}}=\dfrac{2}{\sqrt{2}}}$

$\mathsf{x\;\dfrac{1}{\sqrt{2}}+y\;\dfrac{1}{\sqrt{2}}=\sqrt{2}}$

$\mathsf{x\;cos45^{\circ}+y\;sin45^{\circ}=\sqrt{2}}$

$\textsf{This equation is of the form}\;\mathsf{x\;cos\alpha+y\,sin\alpha=p}$

Find more:

Reduce the equation root 3x+y+2=0 to 1)slope intercept form 2)intercept form and 3) normal form

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