How do you write an equation of a line with point (3,-3) slope 3?

Oct 29, 2017

$y = 3 x - 12$

Explanation:

We can simply apply the formula; $y - {y}_{1} = m \left(x - {x}_{1}\right)$
Where ${x}_{1}$ and ${y}_{1}$ are points on the line, and m is the gradiant

Hence $y - \left(- 3\right) = 3 \left(x - 3\right)$
$\therefore$$y + 3 = 3 x - 9$

Hence when rearanging to yields; $y = 3 x - 12$

Oct 29, 2017

$y = 3 x - 12$

Explanation:

$\text{the equation of a line in "color(blue)"slope-intercept form}$ is.

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{y = m x + b} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

$\text{where m is the slope and b the y-intercept}$

$\text{here } m = 3$

$\Rightarrow y = 3 x + b \leftarrow \textcolor{b l u e}{\text{is the partial equation}}$

$\text{to find b substitute "(3,-3)" into the partial equation}$

$- 3 = 9 + b \Rightarrow b = - 12$

$\Rightarrow y = 3 x - 12 \leftarrow \textcolor{red}{\text{in slope-intercept form}}$

Oct 29, 2017

The answer is $y = 3 x - 12$.

Explanation:

I am assuming that you need this in slope-intercept form. You already know that the slope is $3$. Since the slope-intercept form is

$y = m x + b$

you can fill in $m$ with $3$. Now you have:

$y = 3 x + b$

Now, all that you need to do is solve for $b$. There are two ways to do this. The way that I personally prefer is changing the slope into a fraction.

So first you change $3$ into $\frac{3}{1}$. The next step is to find the reciprocal of $\frac{3}{1}$. This is $\frac{1}{3}$. Now you just subtract $1$ from $3$ until you get zero. Then you take the number of times you had to do this $\left(3\right)$ and multiply it by your denominator, $3$, and add it to $y$ $\left(- 3\right)$. Now you have your $y$-intercept $\left(b\right)$. It is $\left(0 , - 12\right)$.

Another way to do this is by plugging in $x$ and $y$. Here's how to do it:

$y = 3 x + b$

$- 3 = 3 \left(3\right) + b$

$- 3 = 9 + b$

$- 12 = b$

Now just plug in $b$ into your equation and you have:

$y = 3 x - 12$