Question 83198
If you graph {{{y=3x-2 }}} you get

{{{ graph( 300, 200, -5, 5, -5, 5, 3x-2) }}}


If you graph {{{y=-2x+1 }}} you get

{{{ graph( 300, 200, -5, 5, -5, 5,-2x+1) }}}


Since neither of these graphs share the same slope or y-intercept, they are not in a family (ie they have nothing in common). 

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If you graph {{{y=-2x+3 }}} you get

{{{ graph( 300, 200, -5, 5, -5, 5,-2x+3) }}}



and if you graph {{{y=2x+3 }}} you get

{{{ graph( 300, 200, -5, 5, -5, 5,2x+3) }}}


You will notice that these two graphs have the same y-intercept, so they belong in a family (since they share the same y-intercept).



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If you have {{{y=x-3}}} and you want a steeper, negative slope, simply make the slope a large negative value (for the general slope-intercept equation {{{y=mx+b}}}, m is the slope) . So I could choose -7, and that would make a steep, negative slope. So if I graphed {{{y=-7x-3}}} I would get


{{{ graph( 300, 200, -5, 5, -5, 5, -7x-3) }}}


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*[invoke calculating_slope 3, -3, 5, 1]