Question

which equation represents the line shown in the graph? y = -\frac{2}{7}x - 3 y = -\frac{2}{7}x + 3 y = -\frac{7}{2}x + 3 y = -\frac{7}{2}x - 3

Explanation:

Step1: Find the y - intercept

The line crosses the y - axis at the point (0, 3), so the y - intercept $b = 3$.

Step2: Find the slope

Pick two points on the line, say (0, 3) and (2, - 4). The slope $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{-4 - 3}{2-0}=\frac{-7}{2}=-\frac{7}{2}$.

Step3: Use the slope - intercept form

The slope - intercept form of a line is $y=mx + b$. Substituting $m =-\frac{7}{2}$ and $b = 3$ gives $y=-\frac{7}{2}x+3$.

Answer:

$y =-\frac{7}{2}x + 3$