Answer
The equation of the line is $y=2x-1$
Refer to the image below for the graph.
Work Step by Step
RECALL:
(1) The slope-intercept form of a line is $y=mx+b$ where $m$ = slope of the line and $b$ = y-intercept of the line.
(2) Parallel lines have equal or the same slopes.
The line is parallel to the line $y=2x+1$, whose slope is $2$.
This means that the line also has a slope of $2$.
Thus, the tentative equation of the line is:
$y=mx+b
\\y=2x+b$
The line contains the point $(3, 5)$.
This means that the x and y values of this point satisfy the equation of the line.
Substitute the x and y values of this point into the line's tentative equation above to obtain:
$y=2x+b
\\5 = 2(3) + b
\\5 = 6+b
\\5-6=b
\\-1=b$
Thus, the equation of the line is:
$y=2x+(-1)
\\\color{blue}{y=2x-1}$
To graph the line, perform the following steps:
(1) Plot the y-intercept point $(0 ,-1)$.
(2) Plot the point on the line $(3, 5)$.
(3) Connect the two points using a straight line to complete the graph.
(refer to the image in the answer part above for the graph)
