Solver FIND a line by slope and one point

Source code of 'FIND a line by slope and one point'

This Solver (FIND a line by slope and one point) was created by by ichudov(507)

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==section input
Find equation of a line going through point (*[input x1=2], *[input y1=1]) 
that has a slope of *[input slope=1].

==section solution
perl

$yi = $y1 - $slope*$x1;

print "
What we know about the line whose equation we are trying to find out:
  <UL>
    <LI>it goes through point ($x1, $y1)</LI>
    <LI>it has a slope of $slope</LI>
  </UL>

First, let's draw a diagram of the coordinate system with point ($x1, $y1) plotted with a little blue dot:

{{{
  drawing( 400, 400, -10, 10, -10, 10,
           grid(1),
           blue( circle( $x1, $y1, 0.2 ) ) )
}}}

<B>Write this down</B>: the formula for the equation, given point {{{x[1], y[1]}}} and intercept a, is

{{{y=ax + (y[1]-a*x[1])}}} (see a paragraph below explaining why this formula is correct)

Given that a=$slope, and {{{system( x[1] = $x1, y[1] = $y1 ) }}}, we have the equation of the line:

{{{y=$slope*x + $yi}}}

Explanation: <I>Why did we use formula {{{y=ax + (y[1] - a*x[1])}}} ? Explanation goes here. We are trying to find equation y=ax+b. The value of slope (a) is already given to us. We need to find b. If a point ({{{x[1]}}}, {{{y[1]}}}) lies on the line, it means that it satisfies the equation of the line. So, our equation holds for ({{{x[1]}}}, {{{y[1]}}}): {{{y[1] = a*x[1]+b}}} Here, we know a, {{{x[1]}}}, and {{{y[1]}}}, and do not know b. It is easy to find out: {{{b=y[1]-a*x[1]}}}. So, then, the equation of the line is: {{{ y=ax+(y[1]-a*x[1]) }}}. </I>

Here's the graph:

{{{
  drawing( 400, 400, -10, 10, -10, 10,
           grid(1),
           graph( 400, 400, -10, 10, -10, 10, $slope*x+$yi ),
           blue( circle( $x1, $y1, 0.2 ) ),
           locate( $x1, $y1, \"($x1, $y1)\" ) )
           )
        }}}
 ";

==section output
yi

==section check
  x1=2 y1=1 slope=1 yi=-1

==section practice

$x1=randint( -5, 5 );
  $y1=randint( -5, 5 );
  $slope = randint( -2, 2 );