Answer:
[tex]Point-Slope \: Form \: (using \: the \: point \: (1,9) \to \boxed{y-9=2x- 2}\\
Slope-Intercept \: Form \to \boxed{y = 2x + 7}\\
Standard \: Form\to\boxed{ 2x - y = - 7}[/tex]
Step-by-step explanation:
[tex]the \: equation \: is \: gotten \: by \: applying : \ \\ (m) = \frac{ y_{2} -y_{1} }{x_{2} - x_{1}} .............(the \: slope) \\ y-y_{1} =m (x- x_{1})..............(point \: slope \: form) \\ y = mx + c..............................(Slope-Intercept \: Form) \\ \alpha x + \beta y = c...................(Standard \: Form) \\ \\ part \: a. \to \\ Point-Slope \: Form \: (using \: the \: point (1, \: 9)): \\ y-y_{1}=m (x- x_{1}) \\ y-9=m (x- 1) \\ but \: m = \frac{ y_{2} -y_{1} }{x_{2} - x_{1}} = \frac{9 - 7}{1 - 0} \\ m = 2. \\ therefore \: the \: required \: equation \: is : \\ \boxed{y-9=2x- 2}. \\ \\ part \: b. \to \\ Slope-Intercept \: Form: \\ since \: m \: is \: already \: given \: then \: we \: apply : \\ y = m(x) + c \\ c = y - m(x) \\ c = 9 - 2(1) \\ c = 7. \\ therefore \: the \: required \: equation \: is : \\ \boxed{y = 2x + 7}. \\ \\ part \: c. \\Standard \: Form: \\ the \: standard \: form \: is \: given \: by : \\ \alpha x + \beta y = c \\ \boxed{ 2x - y = - 7} \\ is \: the \: required \: equation.[/tex]
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