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. $\newline$ $y = 2x + 8$ $\newline$ 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 = 2x + 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

.

Identify Equation: Identify the given equation and the standard form requirement. $\newline$ The given equation is $y = 2x + 8$ . We need to rewrite it in the standard form $Ax + By = C$ , where $A$ , $B$ , and $C$ are integers with a greatest common factor (GCF) of $1$ , and $A$ should be non-negative.
Move Term: Move the term involving $x$ to the other side of the equation to isolate the constant term on one side. $\newline$ To do this, we subtract $2x$ from both sides of the equation: $\newline$ $y - 2x = 2x + 8 - 2x$ $\newline$ This simplifies to: $\newline$ $y - 2x = 8$
Rearrange to Standard Form: Rearrange the terms to match the standard form $Ax + By = C$ . We want the $x$ term first, followed by the $y$ term, so we rewrite the equation as: $-2x + y = 8$
Ensure Non-Negative Coefficient: Ensure that the coefficient of $x$ is non-negative. $\newline$ Since standard form prefers a non-negative $A$ , we multiply the entire equation by $-1$ to make the coefficient of $x$ positive: $\newline$ $-1(-2x + y) = -1(8)$ $\newline$ This simplifies to: $\newline$ $2x - y = -8$
Check GCF: Check if the coefficients have a GCF other than $1$ . The coefficients are $2$ , $-1$ , and $-8$ . The GCF of these numbers is $1$ .
Final Standard Form: Since the GCF is $1$ , we have the equation in standard form. $\newline$ The final standard form of the equation is: $\newline$ $2x - y = -8$

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