Question

which system of equations is best represented by the graph?
$y = \frac{2}{5}x - 8$
$y= -\frac{3}{5}x - 3$
$y = \frac{5}{2}x - 3$
$y= -\frac{5}{3}x - 8$
$y = \frac{2}{5}x - 3$
$y= -\frac{3}{5}x - 8$
$y = \frac{5}{2}x - 8$
$y= -\frac{5}{3}x - 3$

Explanation:

Step1: Recall slope - intercept form

The equation of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept.

Step2: Analyze positive - slope line

For a line with a positive slope ($m>0$), as $x$ increases, $y$ increases. If we assume one of the lines has a positive slope. Check the y - intercepts of the positive - slope lines in the options. A positive - slope line with a y - intercept of approximately $- 3$ has the form $y=\frac{2}{5}x - 3$ (since $\frac{2}{5}>0$).

Step3: Analyze negative - slope line

For a line with a negative slope ($m < 0$), as $x$ increases, $y$ decreases. A negative - slope line with a y - intercept of approximately $-8$ has the form $y=-\frac{3}{5}x - 8$ (since $-\frac{3}{5}<0$).

Answer:

C. $y=\frac{2}{5}x - 3$, $y =-\frac{3}{5}x - 8$