Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Rewrite the following equation in standard form. $\newline$ $y = 6x + 8$ $\newline$ Hint: The standard form of a linear equation is $Ax + By = C$ where $A$ and $B$ are not both zero, and $A$ , $B$ , and $C$ are integers whose GCF is $1$ .

View step-by-step help

View step-by-step help

Write linear equations in standard form

Full solution

Q. Rewrite the following equation in standard form.

\newline

y = 6x + 8

\newline

Hint: The standard form of a linear equation is

Ax + By = C

where

A

and

B

are not both zero, and

A

,

B

, and

C

are integers whose GCF is

1

.

Start with given equation: To rewrite the equation in standard form, we need to move all terms involving variables to one side of the equation and the constant to the other side. We start with the given equation: $\newline$ $y = 6x - 8$
Move x-term to left: We want to get the equation into the form $Ax + By = C$ . To do this, we will subtract $6x$ from both sides of the equation to move the x-term to the left side: $\newline$ $y - 6x = -8$
Rearrange terms: However, the standard form typically has the $x$ -term before the $y$ -term, so we should rearrange the terms to reflect this: $\newline$ $-6x + y = -8$
Make A positive: Now, we have the equation in the form $Ax + By = C$ , but we need to ensure that $A$ is a positive integer. To do this, we can multiply the entire equation by $-1$ to get the $A$ term positive: $\newline$ $(-1)(-6x) + (-1)(y) = (-1)(-8)$ $\newline$ $6x - y = 8$
Check coefficients: Finally, we check that the coefficients $A$ , $B$ , and $C$ are integers whose greatest common factor (GCF) is $1$ . In this case, the coefficients are $6$ , $-1$ , and $8$ . The GCF of these numbers is $1$ , so we have the equation in the correct form.

More problems from Write linear equations in standard form

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