1. Dana je družina linearnih funkcij: $f(x)=m x+r x-2 m+r+1$. Poišči vrednosti parametrov $m$ in $r$ tako, da bo graf izbrane linearne funkcije vzporeden premici $y=-x$ in bo potekal skozi točko $T(0,3)$.

The family of linear functions is given by: $f(x)=m x+r x-2 m+r+1$. Find the values of the parameters $m$ and $r$ such that the graph of the chosen linear function is parallel to the line $y=-x$ and passes through the point $T(0,3)$.
1. We read the slope of the family of lines $f(x)$. Since the lines are parallel, we equate the slopes of the family of lines and the bisectors of the even quadrants $m+r=-1$. Point $T$ is the intersection of line $\mathrm{z}$ with the y-axis, so we read the y-intercept from the family of functions $f(x)$. We write the equation $-2 m+r+1=3$. We solve the obtained system. The solutions are $m=-1$ and $r=0$.

![](https://cdn.mathpix.com/cropped/2024_06_07_2b0bf3255e176946d93cg-07.jpg?height=54&width=1642&top_left_y=2389&top_left_x=204)

![](https://cdn.mathpix.com/cropped/2024_06_07_2b0bf3255e176946d93cg-07.jpg?height=48&width=1642&top_left_y=2443&top_left_x=204)

![](https://cdn.mathpix.com/cropped/2024_06_07_2b0bf3255e176946d93cg-07.jpg?height=54&width=1639&top_left_y=2486&top_left_x=206)

Solving the system...........................................................................................................................

![](https://cdn.mathpix.com/cropped/2024_06_07_2b0bf3255e176946d93cg-07.jpg?height=55&width=1636&top_left_y=2588&top_left_x=210)