# How do you find slope, point slope, slope intercept, standard form, domain and range of a line for Line E (9,-3) (10,3)?

Aug 8, 2018

color(blue)("Slope " = 6, " Point-Slope form "y + 3 = 6(x - 9)

color(green)("Slope - Intercept form "y = 6x - 51, " Standard form "6x - y = 51

color(purple)("Domain "-oo < x < oo, " Range "-oo < f(x) < oo

#### Explanation:

$E \left(9 , - 3\right) , F \left(10 , 3\right)$

color(crimson)("Slope " = (y_2 - y_1) / (x_2 - x_1)

$\text{Slope of } \overline{E F} = \frac{3 - - 3}{10 - 9} = 6$

color(crimson)("Point Slope form of equation " y - y_1 = m (x - x_1)

$\left(y - \left(- 3\right)\right) = 6 \cdot \left(x - 9\right)$

color(crimson)("Slope - Intercept form of equation is " y = mx = c

$y + 3 = 6 x - 54$

$y = 6 x + \left(- 51\right)$

color(crimson)("Standard form of a linear equation is " ax + by = c

$6 x + \left(- y\right) = 51$

Domain : The function has no undefined points nor domain constraints. Therefore, the domain is $- \infty < x < \infty$

Range :
The range of polynomials with odd degrees all the real numbers.
Therefore, range is $- \infty < f \left(x\right) < \infty$