randRangeNonZero( -9, 9 ) randRangeNonZero( -9, 9 ) randRangeNonZero( -9, 9 ) X_COEFF * X_INTERCEPT

Given the equation:

expr([ "*", X_COEFF, "x" ]) + expr([ "*", Y_COEFF, "y" ]) = EQUALS

What is the x-intercept?

^\(\s*X_INTERCEPT\s*,\s*0\s*\)$

a point, like (3, 2)

The x-intercept is the point where the line crosses the x-axis. This happens when y is zero.

Set y to zero and solve for x.

expr([ "*", X_COEFF, "x" ]) + expr([ "*", Y_COEFF, 0 ]) = EQUALS

expr([ "*", X_COEFF, "x" ]) = EQUALS

(fractionReduce( 1, X_COEFF )) \cdot (X_COEFFx) = (fractionReduce( 1, X_COEFF )) \cdot (EQUALS)

x = X_INTERCEPT

This line intersects the x-axis at (X_INTERCEPT, 0).

graphInit({ range: 11, scale: 20, tickStep: 1, labelStep: 1, unityLabels: false, labelFormat: function( s ) { return "\\small{" + s + "}"; }, axisArrows: "<->" }); style({ stroke: BLUE }); plot(function( x ) { return ( -1 * X_COEFF / Y_COEFF ) * x + EQUALS / Y_COEFF; }, [ -11, 11 ] ); circle( [X_INTERCEPT, 0], 3/20, { stroke: BLUE, fill: BLUE } ); label( [X_INTERCEPT, 0], "(" + X_INTERCEPT + ", 0)", "above", { labelDistance: 5 } );