randRangeNonZero( -5, 5 ) randRangeExclude( -5, 5, [ -3, 0, 3 ] ) randRangeNonZero( -5, 5 ) [ -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5 ] $.map( X1, function( x ){ return ( C - A * x ) / B; } ) randRange( -5, 5 ) ( C - A * HINT_X1 ) / B -A / B C / B

Convert the following equation from standard form to point-slope.

expr([ '*', A, 'x' ]) + expr([ '*', B, 'y' ]) = C

y - {}{} = {}(x - {})

[ $( '#solution_x' ).val(), $( '#solution_y' ).val(), $( '#solution_m' ).val() ]
var answer_x = guess[ 0 ]; var answer_y = guess[ 1 ]; var answer_slope = guess[ 2 ]; return abs( ( ( C - A * answer_x ) / B ) - answer_y ) < 0.001 && abs( answer_slope - SLOPE ) < 0.001;
$( '#solution_x' ).val( guess[ 0 ] ); $( '#solution_y' ).val( guess[ 1 ] ); $( '#solution_m' ).val( guess[ 2 ] );

integers, like 6

simplified proper fractions, like 3/5

simplified improper fractions, like 7/4

and/or exact decimals, like 0.75

pay attention to the sign of each number you enter to be sure the entire equation is correct

Point-slope form is:

\qquad y - \color{BLUE}{y_{1}} = \color{PINK}{m}(x-\color{BLUE}{x_{1}})

\qquadwhere m is the slope and (x_{1}, y_{1}) is any point on the line.

Find the slope of the line:

\color{PINK}{m} = -\dfrac{A}{B} = -\dfrac{A}{B} = \color{PINK}{SLOPE}

We can pick any point we want on the line by plugging in any value for x_{1}. For example, let's choose HINT_X1.

Plug in HINT_X1 as the value of x in the original equation in order to get y_{1}.

A\color{BLUE}{(HINT_X1)} +- abs( B )\color{BLUE}{y_1} = C

y_1 = ( -A * HINT_X1 + C ) / B

Thus, the equation can be written in point-slope form as:

\qquad y - \color{BLUE}{(HINT_Y1)} = \color{PINK}{SLOPE}(x - \color{BLUE}{(HINT_X1)})

\qquad plus( "y", -HINT_Y1 ) = - abs( SLOPE )( plus( "x", -HINT_X1 ) )

Behold the magic of math! The given point (HINT_X1,HINT_Y1) is on the line with slope SLOPE!

graphInit({ range: 10, scale: 20, axisArrows: "<->", tickStep: 1, labelStep: 1 }); style({ stroke: BLUE, fill: BLUE }); plot(function( x ) { return x * SLOPE + Y_INTERCEPT; }, [ -10, 10 ]); circle([HINT_X1,HINT_Y1], .25);
randRangeNonZero( -5, 5 ) randRangeNonZero( -5, 5 ) randRangeNonZero( -5, 5 ) SLOPE < 0 ? -SLOPE : SLOPE SLOPE < 0 ? 1 : -1 SLOPE < 0 ? Y1 - SLOPE * X1 : SLOPE * X1 - Y1 C / B

Convert the following equation from point-slope to standard form.

y - Y1 = SLOPE -( x - X1 )

In other words, rewrite the equation in the form Ax + By = C. Assume A is positive.

A\space x + {} B\space y = {} C

three integers to complete the standard form equation
assume that A is positive

Distribute the SLOPE on the right side of the equation.

expr([ '+', "y", -1 * Y1 ]) = expr([ '*', SLOPE, "x" ]) - SLOPE * X1

Move the expr([ '*', SLOPE, "x" ]) term to the left side of the equation.

expr([ '*', -SLOPE, "x" ]) + y - Y1 = -SLOPE * X1

Move the constant of -1 * Y1 to the right side of the equation.

expr([ '*', -SLOPE, "x" ]) + y = ( -SLOPE * X1 ) + Y1

Multiply both sides by -1.

expr([ '*', SLOPE, "x" ]) - y = -Y1 + ( SLOPE * X1 )

The equation is now in standard form.

Behold the magic of math! The line expr([ '*', SLOPE, "x" ]) - y = -Y1 + ( SLOPE * X1 ) expr([ '*', -SLOPE, "x" ]) + y = ( -SLOPE * X1 ) + Y1 has a slope of SLOPE and passes through the point (X1,Y1). These values were given in the initial equation written in point slope form.

graphInit({ range: 10, scale: 20, axisArrows: "<->", tickStep: 1, labelStep: 1 }); style({ stroke: BLUE, fill: BLUE }); plot( function( x ) { return x * SLOPE + Y_INTERCEPT; }, [ -10, 10 ] ); circle( [ X1, Y1 ], .25 );