Answer
$y=3x-1$, or, in general form, $3x-y-1=0$
Work Step by Step
Through $(1,2);$ parallel to the line $y=3x-5$
Use the point-slope form of the equation of a line, which is $y-y_{1}=m(x-x_{1})$, where $(x_{1},y_{1})$ is a point through which the line passes and $m$ is the slope.
$(x_{1},y_{1})$ and the equation of a line parallel to the line we have to find are given.
Parallel lines have the same slope. The line given is written in slope-intercept form, so we can identify its slope as $3$ and this is also the slope of the line we have to find.
Substitute $(x_{1},y_{1})$ and $m$ into the formula and simplify to obtain the equation of the line we have to find:
$y-y_{1}=m(x-x_{1})$
$y-2=3(x-1)$
$y-2=3x-3$
$y=3x-3+2$
$y=3x-1$, or, in general form, $3x-y-1=0$
