Question

use the given conditions to write an equation for the line in point - slope form. passing through (7, 2) and (4, 3) \\(\circ\\) \\(y - 2 = -\frac{1}{3}(x - 4)\\) or \\(y - 3 = -\frac{1}{3}(x - 7)\\) \\(\circ\\) \\(y - 2 = -\frac{1}{3}(x - 7)\\) or \\(y - 3 = -\frac{1}{3}(x - 4)\\) \\(\circ\\) \\(y - 2 = 7(x + 7)\\) or \\(y - 3 = 4(x - 2)\\) \\(\circ\\) \\(y + 2 = -\frac{1}{3}(x + 7)\\) or \\(y + 3 = -\frac{1}{3}(x + 4)\\)

Explanation:

Step1: Calculate the slope

The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$. Using points $(7,2)$ and $(4,3)$:
$m = \frac{3 - 2}{4 - 7} = \frac{1}{-3} = -\frac{1}{3}$

Step2: Apply point-slope form

Point-slope form is $y - y_1 = m(x - x_1)$.
For point $(7,2)$: $y - 2 = -\frac{1}{3}(x - 7)$
For point $(4,3)$: $y - 3 = -\frac{1}{3}(x - 4)$

Answer:

$\boldsymbol{y - 2 = -\frac{1}{3}(x - 7) \text{ or } y - 3 = -\frac{1}{3}(x - 4)}$ (second option)