Question

which equation is a point slope form equation for line ab?
\\( y - 1 = \frac{3}{4}(x - 2) \\)
\\( y - 6 = \frac{3}{4}(x - 5) \\)
\\( y - 5 = \frac{3}{4}(x - 6) \\)
\\( y - 2 = \frac{3}{4}(x - 1) \\)
graph of line ab with points a and b plotted on a coordinate grid

Explanation:

Step1: Identify points on line AB

From the graph, point A is $(x_1,y_1)=(2,1)$ and point B is $(x_2,y_2)=(6,4)$.

Step2: Calculate the slope

Use slope formula $m=\frac{y_2-y_1}{x_2-x_1}$
$m=\frac{4-1}{6-2}=\frac{3}{4}$

Step3: Apply point-slope form

Point-slope formula: $y-y_1=m(x-x_1)$. Using point A $(2,1)$:
$y-1=\frac{3}{4}(x-2)$
Verify with point B $(6,4)$: $y-4=\frac{3}{4}(x-6)$, which is not an option. The valid option uses point A.

Answer:

$y - 1 = \frac{3}{4}(x - 2)$