Instructions:

$-$ Step $1$: Write the C source code $($named as $"$pe$2.$c$")$ with vim by using the command: vim pe$2.$c

$($a$)$ Write a function to find and return the slope of a line. The equation to calculate the slope from two points is given as: $\backslash ($ m$=\backslash$frac$\{$y$\_\{2\}-$y$\_\{1\}\}\{$x$\_\{2\}-$x$\_\{1\}\}\backslash ).$ Call this function twice to compute $\backslash ($ m$\_\{1\}\backslash )$ and $\backslash ($ m$\_\{2\}\backslash ).$

$($b$)$ Write a function to find and return the y $-$intercept of a line. Note that the y intercept of a line is the value of y at the point where the line crosses the y axis, i$.$e$.,$ when $\backslash ($ x$=0\backslash ).$ Call this function twice to compute $\backslash ($ b$\_\{1\}\backslash )$ and $\backslash ($ b$\_\{2\}\backslash ).$

$($c$)$ Write a function to compute and return the angle between the two lines. Note that the angle $\backslash (\backslash$theta $\backslash )$ between the lines having slope $\backslash ($ m$\_\{1\}\backslash )$ and $\backslash ($ m$\_\{2\}\backslash )$ is given by $\backslash (\backslash$theta$=\backslash )\backslash (\backslash$arctan $\backslash$left$(\backslash$frac$\{$m$\_\{1\}-$m$\_\{2\}\}\{1+$m$\_\{1\}$ m$\_\{2\}\}\backslash$right$)\backslash ).$ You may use atan function given in math. $\backslash ($ h $\backslash )$ to compute arctan$.$

$($d$)$ Write a function to print the two line equations, check if the two lines are parallel or intersect using the angle between the two lines. Note that if $\backslash (\backslash$theta$<mi>\backslash </mi>$epsilon $\backslash )$ where $\backslash (\backslash$epsilon $\backslash )$ is a predefined small number, we assume the lines are parallel.

$-$ Step $2$: Build your executable program named as $"$pe$2"$ by using the command: gcc $-$o pe$2$ pe$2.$c

$-$ Step $3$: Run the program by using the command: $./$pe$2$

$-$ Step $4$: Test your code with the provided "test$2.$sh$"$ file by using the command: $-/$test$2.$sh pe$2.$c

Note $1$: You should have the "test$2.$sh$"$ in the same directory as your source code.

Note $2$: You should see "PASS" for all the test cases.

$-$ Step $5$: Submit your source code $("$pe$2.$c$")$ to Learn.Hub $($assignment $"$PE$2").$

Sample Result

$```$

Zafers$-$MacBook$-$Pro:src zafer$ $./$fpex

Enter coordinates of two points on line $1[$x$1,$y$1,$x$2,$y$2]$:

$0\mathrm{.}20\mathrm{.}42\mathrm{.}1-\mathrm{.}4$

Enter coordinates of two points on line $2$: $[$x$3,$y$3,$x$4,$y$4]$:

$0\mathrm{.}72\mathrm{.}83\mathrm{.}20$

The equation of l$1$: y $=-0\mathrm{.}42$x$+0\mathrm{.}48.$

The equation of $12$: y $=-1\mathrm{.}12$x$+3\mathrm{.}58.$

l$1$ and l$2$ lines intersect, and the angle between the two lines is $25\mathrm{.}41.$

Zafers$-$MacBook$-$Pro:src zafer$ $./$fpex

Enter coordinates of two points on line $1[$x$1,$y$1,$x$2,$y$2]$:

$1324$

Enter coordinates of two points on line $2$: $[$x$3,$ y$3,$x$4,$y$4]$:

$2604$

The equation of l$1$: y $=1\mathrm{.}00$x$+2\mathrm{.}00.$

The equation of $12$: y $=1\mathrm{.}00$x$+4\mathrm{.}00.$

l$1$ and l$2$ lines are parallel, and the angle between the two lines is $0\mathrm{.}00.$

Zafers$-$MacBook$-$Pro:src zafer$ $./$fpex

Enter coordinates of two points on line $1[$x$1,$y$1,$x$2,$y$2]$:

$1328$

Enter coordinates of two points on line $2$:$[$x$3,$y$3,$x$4,$y$4]$:

$3256$

The equation of $11$: y $=5\mathrm{.}00$x$-2\mathrm{.}00.$

The equation of l$2$: y $=2\mathrm{.}00$x$-4\mathrm{.}00.$

l$1$ and l$2$ lines intersect, and$\_$the angle between the two lines is $15\mathrm{.}26.$

$```$