Question

line j and line k are graphed on the same coordinate grid.
line j has a slope of $-\frac{2}{3}$ and intersects the y-axis at -4.
line k has a different negative slope than line j and intersects the y-axis above line j.

which equation could describe line k?
$y = -\frac{1}{6}x$
$y = -\frac{2}{3}x - 3$
$y = -\frac{1}{2}x - 5$
$y = x + 1$

Explanation:

Step1: Recall slope-intercept form

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

Step2: Identify line j's parameters

For line $j$: $m_j = -\frac{2}{3}$, $b_j = -4$.

Step3: Filter line k's requirements

Line $k$ needs: 1. Negative slope $m_k
eq -\frac{2}{3}$; 2. Y-intercept $b_k > -4$.

Step4: Evaluate each option

• Option 1: $y = -\frac{1}{6}x$: $m = -\frac{1}{6}$ (negative, not $-\frac{2}{3}$), $b = 0$ (0 > -4) → meets requirements.
• Option 2: $y = -\frac{2}{3}x - 3$: $m = -\frac{2}{3}$ (same as line j) → fails.
• Option 3: $y = -\frac{1}{2}x - 5$: $b = -5$ (-5 < -4) → fails.
• Option 4: $y = x + 1$: $m = 1$ (positive) → fails.

Answer:

y = -1/6x