# How do you find slope, point slope, slope intercept, standard form, domain and range of a line for Line G (6,0) (9,6)?

Mar 19, 2017

slope $= 2$

point-slope equation: $y - 0 = 2 \left(x - 6\right)$

slope-intercept equation: $y = 2 x - 12$

standard form equation: $y - 2 x = - 12$

domain: $\left(- \infty , \infty\right)$

range: $\left(- \infty , \infty\right)$

#### Explanation:

The slope, $m$, is:

$m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}} = \frac{6 - 0}{9 - 6}$

This is the change in $y$ between the two points over the change in $x$ between the two points.

Once you have found the slope, pick one of the points and plug it into the point-slope formula:

$y - {y}_{1} = m \left(x - {x}_{1}\right)$

where ${y}_{1}$ is the $y$-coordinate of one of the points and ${x}_{1}$ is the $x$-coordinate of the same point and $m$ is the slope. In this case, it is:

$y - 0 = 2 \left(x - 6\right)$

To find the slope intercept form, just solve for $y$, but in this case, since I picked the point with a $y$ of $0$ and $y - 0 = y$, that is already done so the slope-intercept form is:

$y = 2 x - 12$

The standard form formula is

$a x + b y = c$

This can be found by just subtracting $2 x$ from both sides of the slope-intercept equation to get:

$y - 2 x = - 12$

Lastly, the domain and range of any straight line are negative infinity to positive infinity.

Hope I helped out!