Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

The equation of line $s$ is $y = -4x - \frac{5}{3}$ . Line $t$ includes the point $(-3,3)$ and is parallel to line $s$ . What is the equation of line $t$ ? $\newline$ Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.

View step-by-step help

View step-by-step help

Write an equation for a parallel or perpendicular line

Full solution

Q. The equation of line

s

is

y = -4x - \frac{5}{3}

. Line

t

includes the point

(-3,3)

and is parallel to line

s

. What is the equation of line

t

?

\newline

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

Parallel Lines Slopes: Line $t$ is parallel to line $s$ . $\newline$ Are their slopes the same or different? $\newline$ Slopes of parallel lines are the same.
Equation of Line s: Equation of line s: $\newline$ $y = -4x - \frac{5}{3}$ $\newline$ Find the slope of line s. $\newline$ Compare $y = -4x - \frac{5}{3}$ with $y = mx + b$ . $\newline$ $m = -4$ $\newline$ Slope of line s: $-4$
Slope of Line $t$ : Line $t$ is parallel to $s$ . $\newline$ Slope of line $s$ : $-4$ $\newline$ Find the slope of line $t$ . $\newline$ Since line $t$ is parallel to line $s$ , its slope is also $-4$ . $\newline$ Slope of line $t$ : $-4$
Finding Y-Intercept: For line $t$ : $\newline$ Slope ( $m$ ): $-4$ $\newline$ Point: $(-3, 3)$ $\newline$ Plug these values in $y = mx + b$ and find the y-intercept. $\newline$ $3 = -4(-3) + b$ $\newline$ $3 = 12 + b$ $\newline$ $3 - 12 = b$ $\newline$ $-9 = b$
Equation of Line t: For line t: $\newline$ Slope $m$ : $-4$ $\newline$ y-intercept $b$ : $-9$ $\newline$ What is the equation of the line t in slope-intercept form? $\newline$ Substitute $-4$ for $m$ and $-9$ for $b$ in $y = mx + b$ . $\newline$ $y = -4x - 9$

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