Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

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 $N$ ?

View step-by-step help

View step-by-step help

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 $2$ .

More problems from Write an equation for a parallel or perpendicular line

Question

(0, 4)

satisfy the equation

y = x

?

\newline

Choices: [[yes]][[no]]

Posted 2 months ago

Question

Find the slope of the line

y = -4x + \frac{2}{5}

\newline

Write your answer as an integer or as a simplified proper or improper fraction.

Posted 1 month ago

Question

Rewrite the following equation in slope-intercept form.

\newline

y + 8 = -8(x - 10)

\newline

Write your answer using integers, proper fractions, and improper fractions in simplest form.

\newline

Posted 1 month ago

Question

y

-intercept of the line

14x - 16y = -10

\newline

Write your answer as an integer or as a simplified proper or improper fraction, not as an ordered pair.

\newline

Posted 1 month ago

Question

q

\frac{-2}{3}

r

is perpendicular to

q

. What is the slope of line

r

\newline

Simplify your answer and write it as a proper fraction, improper fraction, or integer.

\newline

\_\_\_\_\_

Posted 1 month ago

Question

Find the slope of the line

y + 3 = -\frac{1}{18}(x + 6)

\newline

Write your answer as an integer or as a simplified proper or improper fraction.

Posted 1 month ago

Question

p

has an equation of

y = -8x + 6

q

, which is perpendicular to line

p

, includes the point

(2, -2)

. What is the equation of line

q

?

\newline

Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.

\newline

Posted 1 month ago

Question

Is the graph of this equation a horizontal or vertical line?

\newline

x = 7

\newline

\newline

\text{(A)horizontal line}

\newline

\text{(B)vertical line}

Posted 2 months ago

Question

Rewrite the following equation in standard form.

\newline

y = -10x + 7

\newline

Hint: The standard form of a linear equation is

\newline

Ax + By = C

A

B

are not both zero, and

A

B

C

are integers whose GCF is

1

Posted 2 months ago

Question

A line with a slope of

9

passes through the point

(9,9)

. What is its equation in point-slope form?

\newline

Use the specified point in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.

\newline

y - \underline{\hspace{1cm}} = \underline{\hspace{1cm}} (x - \underline{\hspace{1cm}})

Posted 1 month ago