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 $y=3x-1$.