Question 1049462
(1) {{{ 4x + 3y - 1 = 0 }}}
(2) {{{ 2x - 5y - 11 = 0 }}}
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(1) {{{ 3y = -4x + 1 }}}
(1) {{{ y = -(4/3)*x + 1/3 }}}
and
(2) {{{ 5y = 2x - 11 }}}
(2) {{{ y = (2/5)*x - 11/5 }}}
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For (2), think of a unit vector in the 1st
quadrant with an angle {{{ a }}} that has
{{{ tan(a) = 2/5 }}}
{{{ a = arctan( .4 ) }}}
{{{ a = 21.8014 }}} degrees
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Think of (1) as a unit vector in the 4th quadrant
with {{{ tan(b) = -4/3 ) }}}
{{{ b = arctan( -4/3) }}}
{{{ b = -53.1301 }}}
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The angle between the lines is:
{{{ a - b = 21.8014 + 53.1301 }}}
{{{ a - b = 74.9315 }}} degrees is
the acute angle between the lines
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Here's the plot of lines:
{{{ graph( 500, 500, -10, 10, -10, 10, -(4/3)*x + 1/3, (2/5)*x + 11/5 ) }}}
My answer looks possible