# How do you find an equation for each line with slope -5 passing through the point (3,4)?

##### 1 Answer
Feb 11, 2017

See the entire solution process below:

#### Explanation:

We can use the point-slope formula to find an equation for this line. The point-slope formula states: $\left(y - \textcolor{red}{{y}_{1}}\right) = \textcolor{b l u e}{m} \left(x - \textcolor{red}{{x}_{1}}\right)$

Where $\textcolor{b l u e}{m}$ is the slope and $\textcolor{red}{\left(\left({x}_{1} , {y}_{1}\right)\right)}$ is a point the line passes through.

Substituting the information from the problem gives:

$\left(y - \textcolor{red}{4}\right) = \textcolor{b l u e}{- 5} \left(x - \textcolor{red}{3}\right)$

Or we can convert to the slope-intercept form by solving for $y$. The slope-intercept form of a linear equation is: $y = \textcolor{red}{m} x + \textcolor{b l u e}{b}$

Where $\textcolor{red}{m}$ is the slope and $\textcolor{b l u e}{b}$ is the y-intercept value.

$y - \textcolor{red}{4} = \left(\textcolor{b l u e}{- 5} \times x\right) - \left(\textcolor{b l u e}{- 5} \times \textcolor{red}{3}\right)$

$y - \textcolor{red}{4} = - 5 x + 15$

$y - \textcolor{red}{4} + 4 = - 5 x + 15 + 4$

$y - 0 = - 5 x + 19$

$y = \textcolor{red}{- 5} x + \textcolor{b l u e}{19}$

Or, we can transform this equation into standard 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

$5 x + y = 5 x + \textcolor{red}{- 5} x + \textcolor{b l u e}{19}$

$5 x + y = 0 + 19$

$\textcolor{red}{5} x + \textcolor{b l u e}{1} y = \textcolor{g r e e n}{19}$