Chapter 4: Q18. (page 244)

Write each equation in standard form.
$y + 4 = \frac{2}{3} (x - 3)$

Short Answer

Expert verified

The equation in standard form is $2 x - 3 y = 18$ .

Step by step solution

Step 1. State the concept of the standard form of an equation.

The standard form of a linear equation is $A x + B y = C$ where $A \geq 0$ , $A$ and $B$ are not both zero, and $A, B$ and $C$ are integers with a greatest common factor of 1.

The slope-intercept form of a linear equation is $y = m x + b$ , where $m$ is the slope and $b$ is the $y$ -intercept.

Step 2. Simplify the equation.

In order to simplify $y + 4 = \frac{2}{3} (x - 3)$ , first multiply both sides by 3 and then apply the distributive property.

$3 \times (y + 4) = 3 \times \frac{2}{3} (x - 3) 3 \times (y + 4) = 2 \times (x - 3) 3 y + 12 = 2 x - 6$

Step 3. Write the equation in standard form.

Further, simplify the equation so as to rewrite the equation in the needed form of $A x + B y = C$ .

$3 y + 12 = 2 x - 6 3 y + 12 - 12 = 2 x - 6 - 12 Subtract12fromeachside 3 y - 2 x = 2 x - 18 - 2 x Subtract 2 x fromeachside (- 1) \times (3 y - 2 x) = (- 1) \times (- 18) Multiplybothsidesby-1 2 x - 3 y = 18$

Thus, the equation in standard form is $2 x - 3 y = 18$ .

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Write each equation in standard form.
$y + 4 = \frac{2}{3} (x - 3)$

Short Answer

Step by step solution

Step 1. State the concept of the standard form of an equation.

Step 2. Simplify the equation.

Step 3. Write the equation in standard form.

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Write each equation in standard form.y+4=23x−3

Short Answer

Step by step solution

Step 1. State the concept of the standard form of an equation.

Step 2. Simplify the equation.

Step 3. Write the equation in standard form.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

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Study anywhere. Anytime. Across all devices.

Write each equation in standard form.
$y + 4 = \frac{2}{3} (x - 3)$