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Line
M has equation
y=2x+5. If line
N is parallel to line
M and the graph of line
N in the
xy plane passes through the point
(3,8), what is the
y coordinate of the
y-intercept of line
N ?

Line $M$ has equation $y=2 x+5$ . If line $N$ is parallel to line $M$ and the graph of line $N$ in the $x y$ plane passes through the point $(3,8)$ , what is the $y$ coordinate of the $y$ -intercept of line $N$ ?

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Write an equation for a parallel or perpendicular line

Full solution

Q. Line

M

has equation

y=2 x+5

. If line

N

is parallel to line

M

and the graph of line

N

in the

x y

plane passes through the point

(3,8)

, what is the

y

coordinate of the

y

-intercept of line

N

?

Identify slope of line M: Identify the slope of line M, since line N is parallel to M, they share the same slope. Equation of line M is $y = 2x + 5$ , so the slope ( $m$ ) is $2$ .
Use point-slope form: Use the point-slope form of the equation to find the equation of line $N$ . Point $(3,8)$ lies on line $N$ . Using the slope from line $M$ , which is $2$ , the equation becomes $y - 8 = 2(x - 3)$ .
Simplify equation of line N: Simplify the equation of line N. Start with $y - 8 = 2(x - 3)$ , then $y - 8 = 2x - 6$ , and finally $y = 2x + 2$ . This is the equation of line N in slope-intercept form, where the y-intercept $(b)$ is $2$ .

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