randRangeNonZero(-10, 10) randRangeNonZero(-10, 10) randRangeNonZero(-10, 10) randRangeNonZero(-10, 10) abs(X1 - X2)/2 abs(Y1 - Y2)/2 max(X1, X2) + X_MARGIN min(X1, X2) - X_MARGIN max(Y1, Y2) + Y_MARGIN min(Y1, Y2) - Y_MARGIN Y1 - Y2 X1 - X2 SLOPE_NUMERATOR / SLOPE_DENOMINATOR Y1 - (X1 * M)

The following line passes through point `(X1, Y1)`:

`y = fractionReduce(SLOPE_NUMERATOR, SLOPE_DENOMINATOR) x + b`

What is the value of the `y`-intercept `b`?

`b =` (Y1 * SLOPE_DENOMINATOR - X1 * SLOPE_NUMERATOR) / SLOPE_DENOMINATOR

Substituting `(X1, Y1)` into the equation gives:

`Y1 = fractionReduce(SLOPE_NUMERATOR, SLOPE_DENOMINATOR) \cdot X1 + b`

`Y1 = fractionReduce(X1 * SLOPE_NUMERATOR , SLOPE_DENOMINATOR) + b`

`b = Y1 - fractionReduce(X1 * SLOPE_NUMERATOR , SLOPE_DENOMINATOR)`

`b = fractionReduce(Y1 * SLOPE_DENOMINATOR - X1 * SLOPE_NUMERATOR, SLOPE_DENOMINATOR)`

Plugging in `fractionReduce(Y1 * SLOPE_DENOMINATOR - X1 * SLOPE_NUMERATOR, SLOPE_DENOMINATOR)` for `b`, we get `y = fractionReduce(SLOPE_NUMERATOR, SLOPE_DENOMINATOR) x + fractionReduce(Y1 * SLOPE_DENOMINATOR - X1 * SLOPE_NUMERATOR, SLOPE_DENOMINATOR)`.

graphInit({ range: max(abs(B) + 4, 11), scale: 220 / max(abs(B) + 4, 11), tickStep: ceil(max(abs(B) + 4, 11) / 11), labelStep: 1, unityLabels: false, labelFormat: function(s) { return "\\small{" + s + "}"; }, axisArrows: "<-&rt;" }); plot(function(x) { return M * x + B; }, [min((-abs(B) -5), -12) , max((abs(B) + 5), 12)], { stroke: "#28ae7b" }); circle([X1, Y1], 4 / 20, { stroke: "none", fill: "black" }); var p1Position = "above right"; if ((Y1 > Y2) && (X1 > X2)) { p1Position = "below right"; } else if ((Y1 > Y2) && (X1 < X2)) { p1Position = "below left"; } else if ((Y1 < Y2) && (X1 < X2)) { p1Position = "above left"; } label([X1, Y1], "(" + X1 + ", " + Y1 + ")", p1Position);
randRangeNonZero(-10, 10) randRangeNonZero(-10, 10) randRangeNonZero(-10, 10) Y_COEFF * Y_INTERCEPT

Given the line:

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

What is the `y`-intercept?

`\large(0,\` Y_INTERCEPT`\large)`

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

Set `x` to zero and solve for `y`:

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

`expr(["*", Y_COEFF, "y"]) = EQUALS`

`\dfrac{Y_COEFFy}{Y_COEFF} = \dfrac{EQUALS}{Y_COEFF}`

`y = Y_INTERCEPT`

The line intersects the `y`-axis at `(0, Y_INTERCEPT)`.

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([0, Y_INTERCEPT], 4 / 20, { stroke: BLUE, fill: BLUE }); label([0, Y_INTERCEPT], "(0, " + Y_INTERCEPT + ")", "right", { labelDistance: 5 });