# Khan/khan-exercises

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 Interpreting linear relationships
randRange( 0, 2 ) 1 / randRange( 2, 5 ) randRange( 1, 3 ) [ deskItem( 0 ), fruit( 0 ), "X" ][ INDEX ] [ i18n._("# of %(unit)s", {unit: plural_form( UNIT )}), i18n._("# of %(unit)s", {unit: plural_form( UNIT )}), "X" ][ INDEX ] [ i18n._("Cost of producing %(unit)s", {unit: plural_form( UNIT )}), i18n._("Cost of producing %(unit)s", {unit: plural_form( UNIT )}), "Y" ][ INDEX ] i18n._("black arrow") i18n._("green arrow")

How does Y change as X increases?

How does the cost of producing plural_form(UNIT) change as the number of plural_form(UNIT) increases?

init({ range: [[-3, 10], [-1, 10]], scale: [30, 30] }); grid( [10, 10], [10, 10], { stroke: "#ccc" }); style({ stroke: "#888", strokeWidth: 2, arrows: "->" }); path( [ [-0.5, 0], [10, 0] ] ); path( [ [0, -0.5], [0, 10] ] ); style({ stroke: BLACK, strokeWidth: 0.9, arrows: "->" }); label( [ 0, 9.2 ], "\\text{" + Y_AXIS_LABEL + "}", "right"); label( [ 8.5, 0], "\\text{" + X_AXIS_LABEL + "}", "below"); style({ stroke: BLUE, strokeWidth: 2, arrows: "->" }); plot( function( x ) { return ( M ) * x + B; }, [0, 10]);
Increases
• Increases
• Decreases
• Stays the same
style({ fill: "", stroke: BLACK }); line( [ 4, 4 * M + B ], [ 7, 4 * M + B ] ); style({ stroke: GREEN }); line( [ 7, 4 * M + B ], [ 7, 7 * M + B ] );

Looking at the graph, we see that as x increases (\text{BLACK_ARROW}), y also increases (\green{\text{GREEN_ARROW}}).

We can say that the slope of the line is positive, or that the variables have a direct relationship.

Thus, as X increases, Y also increases.

Thus, as the number of plural_form(UNIT) increases, the price of plural_form(UNIT) also increases.

1 / randRange( 2, 5 ) * -1 randRange( 6, 8 ) i18n._("black arrow") i18n._("red arrow")
Decreases
style({ fill: "", stroke: "#000000" }); line( [ 4, 4 * M + B ], [ 7, 4 * M + B ] ); style({ stroke: "#ff0000" }); line( [ 7, 4 * M + B ], [ 7, 7 * M + B ] );

Looking at the graph, we see that as x increases (\text{BLACK_ARROW}), y decreases (\red{\text{RED_ARROW}}).

We can say that the slope of the line is negative, or that the variables have an inverse relationship.

Thus, as X increases, Y decreases.

Thus, as the number of plural_form(UNIT) increases, the price of plural_form(UNIT) decreases.

0 randRange( 2, 8 )
Stays the same

Looking at the graph, we see that as x increases, there is no change in y.

We can say that the slope of the line is zero, or that the variables have no correlation.

Thus, as X increases, Y stays the same.

Thus, as the number of plural_form(UNIT) increases, the price of plural_form(UNIT) stays the same.