Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Line $e$ has a slope of $\frac{5}{8}$ . Line $f$ has a slope of $\frac{8}{5}$ . Are line $e$ and line $f$ parallel or perpendicular? $\newline$ Choices: $\newline$ (A) parallel $\newline$ (B) perpendicular $\newline$ (C) neither

View step-by-step help

View step-by-step help

Slopes of parallel and perpendicular lines

Full solution

Q. Line

e

has a slope of

\frac{5}{8}

. Line

f

has a slope of

\frac{8}{5}

. Are line

e

and line

f

parallel or perpendicular?

\newline

Choices:

\newline

(A) parallel

\newline

(B) perpendicular

\newline

(C) neither

Calculate slopes: Line $e$ slope: $\frac{5}{8}$ . Line $f$ slope: $\frac{8}{5}$ . $\newline$ Check if slopes are negative reciprocals for perpendicularity.
Check negative reciprocals: Negative reciprocal of $\frac{5}{8}$ is $-\frac{8}{5}$ . $\newline$ Line $f$ slope is $\frac{8}{5}$ , which is the positive reciprocal of line $e$ 's slope.
Verify perpendicularity: Since slopes are positive reciprocals, not negative, lines $e$ and $f$ are not perpendicular.
Confirm non-parallel lines: Lines $e$ and $f$ are not parallel either, because their slopes are not equal.

More problems from Slopes of parallel and perpendicular lines

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