Question

(1 point) \\(\circ\\ y = \frac{9}{4}x + \frac{11}{8}\\) \\(\circ\\ y = \frac{11}{8}x + \frac{9}{4}\\) \\(\circ\\ y = \frac{11}{8}x - 2\\) \\(\circ\\ y = \frac{1}{1}x + \frac{11}{1}\\)

Explanation:

Step1: Calculate the slope (m)

The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$. Using the points $(2, 5)$ and $(-6, -6)$:
$m = \frac{5 - (-6)}{2 - (-6)} = \frac{11}{8}$

Step2: Use point - slope form to find the equation

Point - slope form is $y - y_1 = m(x - x_1)$. Using the point $(2, 5)$ and $m=\frac{11}{8}$:
$y - 5=\frac{11}{8}(x - 2)$
Expand the right - hand side: $y-5=\frac{11}{8}x-\frac{22}{8}$
Simplify $\frac{22}{8}=\frac{11}{4}$, then $y=\frac{11}{8}x-\frac{11}{4}+5$
Convert 5 to $\frac{20}{4}$, so $y=\frac{11}{8}x+\frac{- 11 + 20}{4}=\frac{11}{8}x+\frac{9}{4}$

Answer:

$y=\frac{11}{8}x+\frac{9}{4}$ (the second option)