Write an equation for the line that is parallel to the given line and that passes through the given point. y = 2x + 7; (3, 11)

Two lines that are parallel have the same slope.  Thus, the slope of the given line is 2 and the slope of the new line is also 2.

General slope-intercept equation of a str. line is y = mx + b.

Let m = 2:  y = 2x + b
This new line passes thru (3,11).  Thus, subst. 3 for x and 11 for y in
y = 2x + b, to find b:

11 = 2(3)+b
11 = 6 + b               so b=5

Thus, the equation of the new line, parallel to the old, is y = 2x + 5.