Question

find The line through the point(3,3)with a slope of -1

Answer 1

Answer on Question #42063 – Math – Analytic Geometry

Question. Find the line through the point $(3,3)$ with a slope of $-1$

Solution. The equation of a line with slope $k$ has the following form:

$y=kx+b$

for some $b$. In our case $k=-1$, so we get the equation

$y=-x+b.$

To find $b$ use the assumption that the line passes through the point $(3,3)$. This means that substituting coordinates of this point into the equation we will get the identity. Thus

$3=-3+b,$

whence

$b=3+3=6.$

Thus the line through the point $(3,3)$ with a slope of $-1$ has the folowing equation:

$y=-x+6.$

Answer. $y=-x+6.$

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