Question

the table of ordered pairs represents some points on line p. line n is shown on the coordinate grid. which system of equations represents line n and line p? options: 1. $3x - y = 2$; $2x + y = 4$ 2. $3x + y = -2$; $2x + y = 4$ 3. $3x - y = 2$; $x + 2y = 4$ (table for line p: x values -1, 0, 1, 2; corresponding y values 6, 4, 2, 0. coordinate grid shows line n with points (1,1) and (0, -2))

Explanation:

Step1: Find equation for Line n

Use points $(1,1)$ and $(0,-2)$. First calculate slope:
$m = \frac{1 - (-2)}{1 - 0} = 3$
Use slope-intercept form $y=mx+b$, $b=-2$, so $y=3x-2$, rearrange to $3x - y = 2$.

Step2: Find equation for Line p

Use points $(0,4)$ and $(1,2)$. Calculate slope:
$m = \frac{2 - 4}{1 - 0} = -2$
Use slope-intercept form $y=mx+b$, $b=4$, so $y=-2x+4$, rearrange to $2x + y = 4$.

Answer:

$\boldsymbol{3x - y = 2}$ and $\boldsymbol{2x + y = 4}$ (first option)