Question 741070
{{{ y = -x }}}
{{{ y = -7x }}}
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These are equations of straight lines which
intersect at some point
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It's a good idea to see what you can about the
lines, just by looking at the equations.
The general form of a straight line is
{{{ y = m*x + b }}} where {{{ m }}} is the slope
of the lines. {{{ b = 0 }}} for both lines, so they
both look like {{{ y = m*x }}}
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{{{ y = (-1)*x }}}
The slope is {{{ -1 }}}
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{{{ y = -7x }}}
The slope is {{{ -7 }}}
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For the first equation, if I say
{{{ x = 0 }}}, then:
{{{ y = (-1)*0 }}}
{{{ y = 0 }}}
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For the 2nd equation, if I say
{{{ x = 0 }}}, then
{{{ y = (-7)*0 }}}
{{{ y = 0 }}}
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I have just shown that both lines pass
through (0,0), which is the origin.
Two straight lines can only intersect at one point,
so, {{{ x = 0 }}}, {{{ y = 0 }}} is the solution
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Here is the plot of the lines:
{{{ graph( 400, 400, -8, 8, -8, 8, -x, -7x ) }}}