Answer
$y=3x-1$
Work Step by Step
RECALL:
(1) Parallel lines have equal slopes.
(2) The slope-intercept form of a line's equation is $y=mx+b$, where $m$ = slope and $b$ = y-intercept.
The line is parallel to the line $y=3x-5$ whose slope is $3$.
This means that line also has a slope of $3$.
Thus, the tentative equation of the line is:
$y=3x+b$
The line passes through the point $(1, 2)$.
To find the value of $b$, substitute the x and y coordinates of this point into the tentative equation above to obtain:
$y=3x+b
\\2=3(1) + b
\\2 = 3 + b
\\2-3 = b
\\-1=b$
Therefore, the equation of the line is $y=3x-1$.
