Straight Line in a Plane and its Directional Angle

Project ID: 
6000000066
Accepted: 
Type: 
Layout: 
Question: 
A straight line $p$ is given by a point $A$ and a direction angle $\varphi$. For each given line choose the correct slope-intercept form equation.
Questions Title: 
Graphs:
Answers Title: 
Equations:
Question 1: 
{\obrA}
Question 1 Image: 
Answer 1: 

$p\colon y=-\sqrt3x+3$

Question 2: 
{\obrB}
Question 2 Image: 
Answer 2: 

$p\colon y=\frac{\sqrt3}3x+3$

Question 3: 
{\obrC}
Question 3 Image: 
Answer 3: 

$p\colon y=\sqrt3x+3$

Question 4: 
{\obrD}
Question 4 Image: 
Answer 4: 

$p\colon y=-x+3$

Question 5: 
{\obrE}
Question 5 Image: 
Answer 5: 

<p>$p\colon y=x+3$</p>

Question 6: 
{\obrF}
Question 6 Image: 
Answer 6: 

$p\colon -\frac{\sqrt3}3x+3$

Answer 7: 

$p\colon y=-2x+3$

Answer 8: 

$p\colon y=2x+3$

Tex: 
% tiket 32953 \NastavOD{4} \def\obrA{\obrMsr[x=0.5cm,y=0.5cm]{-3}{6}{-2}{6} { \footnotesize \coordinate (A) at (0,3); \coordinate (B) at ({3/3^(1/2)},0); \coordinate (C) at (6,0); \obrClip \obrOsaX[above left] \obrOsaY[below right] \obrPopisX[below]{-2,2,4} \obrPopisY[left]{2,4} \obrZnackyX{-1,1,3,5} \obrZnackyY{-1,1,3,5} \obrFce{-3^(1/2)*(\x)+3} \draw[red] (-1,{3^(1/2)+3}) node [below left]{$p$}; \begin{scope}[thick] \obrKrizek[2pt] {A}{above right}{A=[0;3]} \end{scope} \obrUhelB*[1.5cm] ABC \obrUhelBZnacka[xshift=10pt,yshift=6pt] {A}{B}{C}{$\varphi=120^{\circ}$} }} \def\obrB{\obrMsr[x=0.5cm,y=0.5cm]{-7}{3}{-2}{6} { \footnotesize \coordinate (A) at (0,3); \coordinate (B) at ({-9/3^(1/2)},0); \coordinate (C) at (6,0); \obrClip \obrOsaX[above left] \obrOsaY[below right] \obrPopisX[below]{-6,-4,-2,2} \obrPopisY[left]{2,4} \obrZnackyX{-5,-3,-1,1} \obrZnackyY{-1,1,3,5} \obrFce{3^(1/2)/3*(\x)+3} \draw[red] (-1,{-3^(1/2)/3+3}) node [above left]{$p$}; \begin{scope}[thick] \obrKrizek[2pt] {A}{below right}{A=[0;3]} \end{scope} \obrUhelB*[2cm] ABC \obrUhelBZnacka[xshift=25pt,yshift=6pt] {A}{B}{C}{$\varphi=30^{\circ}$} }} \def\obrC{\obrMsr[x=0.5cm,y=0.5cm]{-4}{5}{-2}{6} { \footnotesize \coordinate (A) at (0,3); \coordinate (B) at ({-3/3^(1/2)},0); \coordinate (C) at (6,0); \obrClip \obrOsaX[above left] \obrOsaY[below right] \obrPopisX[below]{-2,2,4} \obrPopisY[left]{2,4} \obrZnackyX{-3,-1,1,3} \obrZnackyY{-1,1,3,5} \obrFce{3^(1/2)*(\x)+3} \draw[red] (1.5,{1.5*3^(1/2)+3}) node [below right]{$p$}; \begin{scope}[thick] \obrKrizek[2pt] {A}{left}{A=[0;3]} \end{scope} \obrUhelB*[1.75cm] ABC \obrUhelBZnacka[xshift=18pt,yshift=4pt] {A}{B}{C}{$\varphi=60^{\circ}$} }} \def\obrD{\obrMsr[x=0.5cm,y=0.5cm]{-3}{7}{-2}{6} { \footnotesize \coordinate (A) at (0,3); \coordinate (B) at ({3},0); \coordinate (C) at (6,0); \obrClip \obrOsaX[above left] \obrOsaY[below right] \obrPopisX[below]{-2,2,4,6} \obrPopisY[left]{2,4} \obrZnackyX{-1,1,3,5} \obrZnackyY{-1,1,3,5} \obrFce{-(\x)+3} \draw[red] (-2,{2+3}) node [below left]{$p$}; \begin{scope}[thick] \obrKrizek[2pt] {A}{above right}{A=[0;3]} \end{scope} \obrUhelB*[1.5cm] ABC \obrUhelBZnacka[xshift=8pt,yshift=6pt] {A}{B}{C}{$\varphi=135^{\circ}$} }} \def\obrE{\obrMsr[x=0.5cm,y=0.5cm]{-5}{5}{-2}{6} { \footnotesize \coordinate (A) at (0,3); \coordinate (B) at (-3,0); \coordinate (C) at (6,0); \obrClip \obrOsaX[above left] \obrOsaY[below right] \obrPopisX[below]{-4,-2,2,4} \obrPopisY[left]{2,4} \obrZnackyX{-3,-1,1,3} \obrZnackyY{-1,1,3,5} \obrFce{(\x)+3} \draw[red] (2,{2+3}) node [below right]{$p$}; \begin{scope}[thick] \obrKrizek[2pt] {A}{below right}{A=[0;3]} \end{scope} \obrUhelB*[1.75cm] ABC \obrUhelBZnacka[xshift=15pt,yshift=4pt] {A}{B}{C}{$\varphi=45^{\circ}$} }} \def\obrF{\obrMsr[x=0.5cm,y=0.5cm]{-2}{10}{-2}{6} { \footnotesize \coordinate (A) at (0,3); \coordinate (B) at ({9/3^(1/2)},0); \coordinate (C) at (6,0); \obrClip \obrOsaX[above left] \obrOsaY[below right] \obrPopisX[below]{2,4,6,8} \obrPopisY[left]{2,4} \obrZnackyX{-3,-1,1,3,5,7,9} \obrZnackyY{-1,1,3,5} \obrFce{-3^(1/2)/3*(\x)+3} \draw[red] (-1.5,{3^(1/2)/3*1.5+3}) node [above right]{$p$}; \begin{scope}[thick] \obrKrizek[2pt] {A}{above right}{A=[0;3]} \end{scope} \obrUhelB*[1.5cm] ABC \obrUhelBZnacka[xshift=3pt,yshift=9pt] {A}{B}{C}{$\varphi=150^{\circ}$} }}