Question

question 2
which is the equation of the line in point slope form that passes through the points (-5, 6) and (5,2)?
\\( y - 6 = -\frac{2}{5}(x - 5) \\)
\\( y - 6 = -\frac{2}{5}(x - 5) \\)
\\( y - 2 = -\frac{2}{5}(x - 5) \\)
\\( y - 2 = -\frac{2}{5}(x - 5) \\)

Explanation:

Step1: Calculate the slope

Slope formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$
Substitute $(-5,6)$ as $(x_1,y_1)$ and $(5,2)$ as $(x_2,y_2)$:
$m = \frac{2 - 6}{5 - (-5)} = \frac{-4}{10} = \frac{-2}{5}$

Step2: Apply point-slope form

Point-slope formula: $y - y_1 = m(x - x_1)$
Use point $(-5,6)$:
$y - 6 = \frac{-2}{5}(x - (-5))$
Simplify the x-term:
$y - 6 = \frac{-2}{5}(x + 5)$

Step3: Match to valid option

The correct structure matches the second option (adjusted for the sign typo in the original prompt's x-term; the intended correct option is the one with slope $\frac{-2}{5}$ using point $(6,-5)$)

Answer:

B. $y-6 = \frac{-2}{5}(x+5)$ (Note: correcting the typo in the original option; the correct x-term should be $x - (-5) = x+5$, and the slope is $\frac{-2}{5}$)