First Principles AI

Solution

For intercepts:

\begin{aligned} y=0&\Rightarrow -5x+10=0\Rightarrow x=2\quad\Rightarrow (2,0)\\ x=0&\Rightarrow y=10\quad\Rightarrow (0,10) \end{aligned}

\boxed{\text{$x$-int }(2,0),\;\text{$y$-int }(0,10)}

\begin{aligned} y=0&\Rightarrow 2x-1=0\Rightarrow x=\frac{1}{2}\quad\Rightarrow \left(\frac{1}{2},0\right)\\ x=0&\Rightarrow y=-1\quad\Rightarrow (0,-1) \end{aligned}

\boxed{\text{$x$-int }\left(\frac{1}{2},0\right),\;\text{$y$-int }(0,-1)}

\begin{aligned} y=0&\Rightarrow \frac{1}{2}x-3=0\Rightarrow x=6\quad\Rightarrow (6,0)\\ x=0&\Rightarrow y=-3\quad\Rightarrow (0,-3) \end{aligned}

\boxed{\text{$x$-int }(6,0),\;\text{$y$-int }(0,-3)}

\begin{aligned} y=0&\Rightarrow 3x+\frac{3}{2}=0\Rightarrow 3x=-\frac{3}{{2}}\Rightarrow x=-\frac{1}{2}\quad\Rightarrow \left(-\frac{1}{2},0\right)\\ x=0&\Rightarrow y=\frac{3}{2}\quad\Rightarrow \left(0,\frac{3}{2}\right) \end{aligned}

\boxed{\text{$x$-int }\left(-\frac{1}{2},0\right),\;\text{$y$-int }\left(0,\frac{3}{2}\right)}