
1. Zapiši enačbo premice, ki je vzporedna premici $y=3-\frac{x}{2}$ in s koordinatnimi osmi tvori trikotnik s ploščino 49.

1. Vzporedne premice imajo enak smerni koeficient $k=-\frac{1}{2}$ Če uporabimo odsekovno obliko enačbe premice $\frac{x}{m}+\frac{y}{n}=1$, je ploščina enaka $S=\frac{|m \cdot n|}{2}$. Iz odsekovne oblike preoblikujemo v
eksplicitno in dobimo $y=-\frac{n}{m} x+n$. Torej je $k=-\frac{n}{m}=-\frac{1}{2}$ in $m=2 n$. Upoštevamo ploščino $S=\frac{|m \cdot n|}{2}$ in dobimo $49=n^{2}$. Imamo dve možnosti: $n=7, m=14$ ali $n=-7, m=-14$. Obstajata dve takšni premici: $\frac{x}{14}+\frac{y}{7}=1$ in $\frac{x}{-14}+\frac{y}{-7}=1$.

![](https://cdn.mathpix.com/cropped/2024_06_07_7bf3e9b12130e254269ag-08.jpg?height=80&width=1642&top_left_y=420&top_left_x=207)

![](https://cdn.mathpix.com/cropped/2024_06_07_7bf3e9b12130e254269ag-08.jpg?height=68&width=1642&top_left_y=480&top_left_x=207)

![](https://cdn.mathpix.com/cropped/2024_06_07_7bf3e9b12130e254269ag-08.jpg?height=60&width=1639&top_left_y=538&top_left_x=206)

![](https://cdn.mathpix.com/cropped/2024_06_07_7bf3e9b12130e254269ag-08.jpg?height=69&width=1639&top_left_y=585&top_left_x=206)

Zapis enačbe $m=2 n$.................................................................................................

![](https://cdn.mathpix.com/cropped/2024_06_07_7bf3e9b12130e254269ag-08.jpg?height=60&width=1639&top_left_y=684&top_left_x=206)

![](https://cdn.mathpix.com/cropped/2024_06_07_7bf3e9b12130e254269ag-08.jpg?height=66&width=1639&top_left_y=732&top_left_x=206)

![](https://cdn.mathpix.com/cropped/2024_06_07_7bf3e9b12130e254269ag-08.jpg?height=79&width=1642&top_left_y=780&top_left_x=204)
