randRangeNonZero( -5, 5 ) randRangeNonZero( -5, 5 ) randRangeNonZero( -5, 5 ) randRangeNonZero( -5, 5 ) randRangeNonZero( -5, 5 ) randRangeNonZero( -5, 5 ) expr(["+", ["*", A1, "x"], ["*", B1, "y"]]) + " = " + C1 expr(["+", ["*", A2, "x"], ["*", B2, "y"]]) + " = " + C2

What do the following two equations represent?

EQ1

EQ2

None of the above
  • Equivalent lines
  • Parallel lines
  • Perpendicular lines
  • None of the above

The slopes are not the same, so the lines are not equivalent or parallel. The slopes are not negative inverses of each other, so the lines are not perpendicular. The correct answer is none of the above.

randRangeNonZero( -5, 5 ) randRangeNonZero( -5, 5 ) randRangeNonZero( -5, 5 ) randRangeNonZero( -5, 5 ) A1 * F B1 * F C1 * F expr(["+", ["*", A1, "x"], ["*", B1, "y"]]) + " = " + C1 expr(["+", ["*", A2, "x"], ["*", B2, "y"]]) + " = " + C2

What do the following two equations represent?

EQ1

EQ2

Equivalent lines
  • Equivalent lines
  • Parallel lines
  • Perpendicular lines
  • None of the above

The above equations turn into the same equation, so they represent the same line.

randRangeNonZero( -5, 5 ) randRangeNonZero( -5, 5 ) randRangeNonZero( -5, 5 ) randRangeNonZero( -5, 5 ) A1 * F B1 * F randRange( -5, 5 ) expr(["+", ["*", A1, "x"], ["*", B1, "y"]]) + " = " + C1 expr(["+", ["*", A2, "x"], ["*", B2, "y"]]) + " = " + C2

What do the following two equations represent?

EQ1

EQ2

Parallel lines
  • Equivalent lines
  • Parallel lines
  • Perpendicular lines
  • None of the above

The slopes are equal, and the y-intercepts are different, so the lines are parallel.

randRangeNonZero( -5, 5 ) randRangeNonZero( -5, 5 ) randRangeNonZero( -5, 5 ) randRange( 1, 5 ) -1 * B1 * F A1 * F randRangeNonZero( -5, 5 ) expr(["+", ["*", A1, "x"], ["*", B1, "y"]]) + " = " + C1 expr(["+", ["*", A2, "x"], ["*", B2, "y"]]) + " = " + C2

What do the following two equations represent?

EQ1

EQ2

Perpendicular lines
  • Equivalent lines
  • Parallel lines
  • Perpendicular lines
  • None of the above

The slopes are negative inverses of each other, so the lines are perpendicular.

init({ range: [[-10, 10], [-10, 10]], scale: [20, 20] }); grid( [-10, 10], [-10, 10], { stroke: "#ccc" }); style({ stroke: "#888", strokeWidth: 2, arrows: "->" }); path( [ [-10, 0], [10, 0] ] ); path( [ [0, -10], [0, 10] ] ); style({ stroke: "#6495ED", arrows: null }); plot( function( x ) { return ( C1 / B1 ) - ( A1 / B1 ) * x; }, [-10, 10]);

Putting the first equation in y = mx + b form gives:

expr(["+", ["*", A1, "x"], ["*", B1, "y"]]) + " = " + C1

expr(["*", B1, "y"]) + " = " + expr(["+", ["*", (-1 * A1), "x"], C1])

"y = " + fractionReduce( -A1, B1 ) + "x + " + fractionReduce( C1, B1 )

plot( function( x ) { return ( C2 / B2 ) - ( A2 / B2 ) * x; }, [-10, 10]);

Putting the second equation in y = mx + b form gives:

expr(["+", ["*", A2, "x"], ["*", B2, "y"]]) + " = " + C2

expr(["*", B2, "y"]) + " = " + expr(["+", ["*", (-1 * A2), "x"], C2])

"y = " + fractionReduce( -A2, B2 ) + "x + " + fractionReduce( C2, B2 )