# How do you find a standard form equation for the line with (-1,3) and parallel to the line 3x+5y=15?

Jul 29, 2017

See a solution process below:

#### Explanation:

First, we need to find the slope of the line. The equation in the problem is Standard Linear form. The standard form of a linear equation is: $\textcolor{red}{A} x + \textcolor{b l u e}{B} y = \textcolor{g r e e n}{C}$

Where, if at all possible, $\textcolor{red}{A}$, $\textcolor{b l u e}{B}$, and $\textcolor{g r e e n}{C}$are integers, and A is non-negative, and, A, B, and C have no common factors other than 1.

$\textcolor{red}{3} x + \textcolor{b l u e}{5} y = \textcolor{g r e e n}{15}$

The slope of an equation in standard form is: $m = - \frac{\textcolor{red}{A}}{\textcolor{b l u e}{B}}$

Therefore, the slope of this line is:

$m = - \frac{\textcolor{red}{3}}{\textcolor{b l u e}{5}}$

Because the problem is to find the equation of a parallel line, the slope of the line in the problem will be the same as the slope of the equation for the solution. We can then substitute this slope into the formula to give:

$\textcolor{red}{3} x + \textcolor{b l u e}{5} y = \textcolor{g r e e n}{C}$

We have a point given in the problem. We can take the values from this point, substitute them for $x$ and $y$ to calculate $\textcolor{g r e e n}{C}$:

$\textcolor{red}{3} x + \textcolor{b l u e}{5} y = \textcolor{g r e e n}{C}$ becomes:

$\left(\textcolor{red}{3} \times - 1\right) + \left(\textcolor{b l u e}{5} \times 3\right) = \textcolor{g r e e n}{C}$

$- 3 + 15 = \textcolor{g r e e n}{C}$

$12 = \textcolor{g r e e n}{C}$

Substituting this solution for $\textcolor{g r e e n}{C}$ into the formula with the slope gives:

$\textcolor{red}{3} x + \textcolor{b l u e}{5} y = \textcolor{g r e e n}{12}$
The text passage contains a mathematical question about finding the standard form equation for a line that is parallel to a given line and passes through a specific point. The passage also provides a detailed solution to this question.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# How do you find a standard form equation for the line with (-1,3) and parallel to the line 3x+5y=15?

Jul 29, 2017

See a solution process below:

#### Explanation:

First, we need to find the slope of the line. The equation in the problem is Standard Linear form. The standard form of a linear equation is: $\textcolor{red}{A} x + \textcolor{b l u e}{B} y = \textcolor{g r e e n}{C}$

Where, if at all possible, $\textcolor{red}{A}$, $\textcolor{b l u e}{B}$, and $\textcolor{g r e e n}{C}$are integers, and A is non-negative, and, A, B, and C have no common factors other than 1.

$\textcolor{red}{3} x + \textcolor{b l u e}{5} y = \textcolor{g r e e n}{15}$

The slope of an equation in standard form is: $m = - \frac{\textcolor{red}{A}}{\textcolor{b l u e}{B}}$

Therefore, the slope of this line is:

$m = - \frac{\textcolor{red}{3}}{\textcolor{b l u e}{5}}$

Because the problem is to find the equation of a parallel line, the slope of the line in the problem will be the same as the slope of the equation for the solution. We can then substitute this slope into the formula to give:

$\textcolor{red}{3} x + \textcolor{b l u e}{5} y = \textcolor{g r e e n}{C}$

We have a point given in the problem. We can take the values from this point, substitute them for $x$ and $y$ to calculate $\textcolor{g r e e n}{C}$:

$\textcolor{red}{3} x + \textcolor{b l u e}{5} y = \textcolor{g r e e n}{C}$ becomes:

$\left(\textcolor{red}{3} \times - 1\right) + \left(\textcolor{b l u e}{5} \times 3\right) = \textcolor{g r e e n}{C}$

$- 3 + 15 = \textcolor{g r e e n}{C}$

$12 = \textcolor{g r e e n}{C}$

Substituting this solution for $\textcolor{g r e e n}{C}$ into the formula with the slope gives:

$\textcolor{red}{3} x + \textcolor{b l u e}{5} y = \textcolor{g r e e n}{12}$
user
The text passage contains a mathematical question about finding the standard form equation for a line that is parallel to a given line and passes through a specific point. The passage also provides a detailed solution to this question.

TYPE: SINGLE_QUESTION_WITH_ANSWER