# How do you write the equation in point slope form given (-1,4) parallel to y=-5x+2?

Apr 18, 2017

$y - 4 = - 5 \left(x + 1\right)$

#### Explanation:

The equation of a line in $\textcolor{b l u e}{\text{point-slope form}}$ is.

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{y - {y}_{1} = m \left(x - {x}_{1}\right)} \textcolor{w h i t e}{\frac{2}{2}} |}}}$
where m represents the slope and $\left({x}_{1} , {y}_{1}\right) \text{ a point on the line}$

$\text{We have to know the following fact}$

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{\text{ parallel lines have equal slopes}} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

$y = - 5 x + 2 \text{ is in slope-intercept form}$

$\text{that is " y=mx+b" where m is slope}$

$\Rightarrow \text{ required slope } = m = - 5$

$\text{using " m=-5" and " (x_1,y_1)=(-1,4)" then}$

$y - 4 = - 5 \left(x - \left(- 1\right)\right)$

$\Rightarrow y - 4 = - 5 \left(x + 1\right) \leftarrow \textcolor{red}{\text{ in point-slope form}}$

Apr 18, 2017

See the entire solution process below:

#### Explanation:

The equation given in the problem is in slope intercept form. 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.

$y = \textcolor{red}{- 5} x + \textcolor{b l u e}{2}$

Therefore the slope of this line is $\textcolor{red}{m = - 5}$

Because the line we are looking for is parallel to this line, by definition, it will have the same slope.

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.

We can substitute the slope of the first line and the values from the point in the first problem to write the equation of the line in point-slope form:

$\left(y - \textcolor{red}{4}\right) = \textcolor{b l u e}{- 5} \left(x - \textcolor{red}{- 1}\right)$

$\left(y - \textcolor{red}{4}\right) = \textcolor{b l u e}{- 5} \left(x + \textcolor{red}{1}\right)$