Question

question 6
in a video game, a coordinate plane is laid on top of the graphics. a rabbit is shown burrowing 2 units to the right and 1.5 units down. this pattern repeats until the rabbit stops at (7, -6).
for the line connecting the coordinates that the rabbit passes through:
*what is the point slope form of the equation?
*what is the standard form of the equation?
select the two that apply.
□ ( y + 6 = -\frac{3}{4}(x - 7) )
□ ( 4x + 3y = 10 )
□ ( 3x + 4y = -3 )
□ ( y = -\frac{3}{4}x + \frac{49}{4} )
□ ( y = -\frac{3}{4}x - \frac{3}{4} )
□ ( y + 6 = -\frac{3}{4}(x - 7) )

Explanation:

Step1: Calculate slope

The rabbit moves 2 right ($\Delta x=2$) and 1.5 down ($\Delta y=-1.5$). Slope $m=\frac{\Delta y}{\Delta x}=\frac{-1.5}{2}=-\frac{3}{4}$.

Step2: Write point-slope form

Use point $(7,-6)$: $y - y_1 = m(x - x_1)$
$y - (-6) = -\frac{3}{4}(x - 7)$ simplifies to $y + 6 = -\frac{3}{4}(x - 7)$.

Step3: Convert to standard form

Start with $y + 6 = -\frac{3}{4}(x - 7)$
Multiply by 4: $4y + 24 = -3(x - 7)$
Expand: $4y + 24 = -3x + 21$
Rearrange to $Ax+By=C$: $3x + 4y = -3$.

Step4: Match options

The valid equations are $y + 6 = -\frac{3}{4}(x - 7)$ and $3x + 4y = -3$.

Answer:

$y + 6 = -\frac{3}{4}(x - 7)$, $3x + 4y = -3$