# How do you find a standard form equation for the line with slope 2/3 that passes through the point (3,6)?

Mar 26, 2018

You may use the standard form of the straight line:

$y = m x + b$, where $m$ is the slope and $b$ the y-intercept

#### Explanation:

The statement gives that $m = \frac{2}{3}$, so we have to find the value of $b$

Now, we also know that the line passes through $\left(3 , 6\right)$, and so:

$6 = \frac{2}{3} \cdot 3 + b$ and then $6 = 2 + b$ and so $b = 4$. The equation of the line is then:

$y = \frac{2}{3} x + 4$

Mar 26, 2018

The standard form is $2 x - 3 y = - 12$

#### Explanation:

Start by finding the slope-intercept form of the equation, then converting that to the standard form.

The slope-intercept form is
$y = m x + b$

The slope $m$ is given as $\frac{2}{3}$, so the equation up to that point is
$y = \frac{2}{3} x + b$

To find $b$, sub in the values for $x$ and $y$ from the ordered pair given in the problem.

$6 = \frac{2}{3} \left(\frac{3}{1}\right) + b$
Solve for $b$

1) Clear the parentheses by multiplying the fractions
$6 = 2 + b$

2) Subtract $2$ from both sides to isolate $b$
$4 = b$

So the slope-intercept form of the equation is
$y = \left(\frac{2}{3}\right) x + 4$ $\leftarrow$ slope-intercept form

Change the slope-intercept form into standard form.

Standard form is
$a x + b y = c$ where $a$ is a positive whole digit

1) Clear the fraction by multiplying all the terms on both sides by $3$ and letting the denominator cancel
$3 y = 2 x + 12$

2) Subtract $2 x$ from both sides to get the $x$ and $y$ terms on the same side
$- 2 x + 3 y = 12$

3) Multiply through by $- 1$ to clear the minus sign
$2 x - 3 y = - 12$ $\leftarrow$ standard form