Question

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

Answer 1

`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 (9, -3), F (10, 3)`

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

`"Slope of " bar(EF) = (3 - -3) / (10 - 9) = 6`

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

`(y - (-3)) = 6 * (x - 9)`

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

`y + 3 = 6x - 54`

`y = 6x + (-51)`

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

`6x + (-y) = 51`

Domain : The function has no undefined points nor domain constraints. Therefore, the domain is `-oo < x < oo`

Range :
The range of polynomials with odd degrees all the real numbers.
Therefore, range is `-oo < f(x) < oo`