Question 737772
First realize that ANY line which is perpendicular to thr given
line will have the same slope, so that is the 1st thing to find.
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The equation {{{ 4x + 3y = 6 }}} is in the standard form. Put
it into the slope-intercept form which is {{{ y = m*x + b }}}
The {{{ m }}} will be the slope of this line.
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{{{ 4x + 3y = 6 }}}
{{{ 3y = -4x + 6 }}}
{{{ y = (-4/3)*x + 2 }}}
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{{{ m = -4/3 }}}
Now find the slope that is perpendicular to this slope
The formula is {{{ m[p] = -1 / m }}}, so
{{{ m[p] = -1 / (-4/3) }}}
{{{ m[p] = 3/4 }}}
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So far, you have:
{{{ y = (3/4)*x + b }}}
You just need to find {{{ b }}}
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You given the point (2,0) also, so just plug this x and y
into the equation and solve for {{{ b }}}
{{{ 0 = (3/4)*2 + b }}}
{{{ 0 = 3/2 + b }}}
{{{ b = -3/2 }}}
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The complete equation is:
{{{ y = (3/4)*x - 3/2 }}}
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Check:
does it go through (2,0)?
{{{ y = (3/4)*x - 3/2 }}}
{{{ 0 = (3/4)*2 - 3/2 }}}
{{{ (3/4)*2 = 6/4 }}}
{{{ 6/4 = 6/4 }}}
OK
Here is the plot of both lines:
{{{ graph( 500, 500, -10, 10, -10, 10, (-4/3)*x + 2, (3/4)*x - 3/2 ) }}}