# How do you write an equation in standard form if the line passes through (3,7) and (0, -2)?

Apr 14, 2018

$3 x - y = 2$

#### Explanation:

We have the value of two points, $\left(3 , 7\right)$ and $\left(0 , - 2\right)$

First, let's find the slope of this line. The formula for slope is $\text{rise"/"run}$ or $\text{change in y"/"change in x}$ or $\frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$.

Since we have the values of two points, we can plug them into the formula:
$\frac{- 2 - 7}{0 - 3}$

Simplify:
$\frac{- 9}{-} 3$

The negatives cancel out and we simplify it:
$3$

Now we can write the equation in point-slope form, shown here:

$y - 7 = 3 \left(x - 3\right)$

To convert to standard form, we first have to convert from point-slope to slope-intercept form, shown here:

So let's simplify:
$y - 7 = 3 x - 9$

Add $7$ on both sides of the equation:
$y - 7 \quad \textcolor{red}{+ \quad 7} = 3 x - 9 \quad \textcolor{red}{+ \quad 7}$

$y = 3 x - 2$

It is now in slope-intercept form.

Now let's convert this to standard form, by making the $y$-intercept by itself, shown here:

$y = 3 x - 2$

Add $2$ to both sides of the equation:
$y \quad \textcolor{red}{+ \quad 2} = 3 x - 2 \quad \textcolor{red}{+ \quad 2}$

$y + 2 = 3 x$

Subtract $y$ on both sides of the equation:
$y + 2 \quad \textcolor{red}{- \quad y} = 3 x \quad \textcolor{red}{- \quad y}$

$2 = 3 x - y$

Switch sides to put in exact standard form:
$3 x - y = 2$

As you can see, it is now in standard form.

For more information on writing an equation in standard form from two points, feel free to watch these videos:

Short video:

Longer video:

Hope this helps!