Question

question 5
using the following coordinates, write the equation of a line in standard form:
(8, 4) and (10, -18).

○ $y - 4 = -11(x - 8)$

○ $y = -11x + 92$

○ $x + 11y = 92$

○ $11x + y = 92$

Explanation:

Step1: Find the slope (m)

The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$. Using the points (8, 4) and (10, -18), we have $x_1 = 8$, $y_1 = 4$, $x_2 = 10$, $y_2 = -18$.
So, $m = \frac{-18 - 4}{10 - 8} = \frac{-22}{2} = -11$.

Step2: Use point - slope form

The point - slope form is $y - y_1 = m(x - x_1)$. Using the point (8, 4) and $m=-11$, we get $y - 4=-11(x - 8)$.

Step3: Convert to slope - intercept form ($y=mx + b$)

Expand the point - slope form: $y - 4=-11x+88$. Then add 4 to both sides: $y=-11x + 92$.

Step4: Convert to standard form ($Ax+By = C$, where $A$, $B$, $C$ are integers and $A\geq0$)

Add $11x$ to both sides of $y=-11x + 92$: $11x + y=92$.

Answer:

D. $11x + y = 92$ (assuming the last option is D, if the options are labeled as A, B, C, D, E with the last one being E, then E. $11x + y = 92$)