Question

Can someone help me with my math? Please, I am begging you! It's due today and I'm confused.

A line goes through the points (0,7) and (1,9). Write the following equation forms:
Point-Slope Form (using the point (1,9):
Slope-Intercept Form:
Standard Form:

Answer 1

`Point-Slope \: Form \: (using \: the \: point \: (1,9) \to \boxed{y-9=2x- 2}\\ </p><p>Slope-Intercept \: Form \to \boxed{y = 2x + 7}\\ </p><p>Standard \: Form\to\boxed{ 2x - y = - 7}`

Explanation:

`the \: equation \: is \: gotten \: by \: applying : \ \\ (m) = ( 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 = ( y_(2) -y_(1) )/(x_(2) - x_(1)) = (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.`

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