Question

identifying an inequality and solution from its graph
which inequality is represented by the graph?
$y > 2x + (3/4)$
$y < 2x + (3/4)$
$y > (1/2)x + (3/4)$
$y < (1/2)x + (3/4)$
on to the inequality?
(graph with points (0, 0.75) and (2, 4.75), dashed line, and arrow directions)

Explanation:

Step1: Find line slope

Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$
$m=\frac{4.75-0.75}{2-0}=\frac{4}{2}=2$

Step2: Get line equation

Use $y=mx+b$, $b=0.75=\frac{3}{4}$
$y=2x+\frac{3}{4}$

Step3: Determine inequality sign

Dashed line, shaded above line: $y > 2x+\frac{3}{4}$

Answer:

$y > 2x + \frac{3}{4}$