Which equation represents the line that passes through the points (6, –3) and (–4, –9)?
A. y + 4 = three-fifths (x + 9)
B. y + 4 = five-thirds(x + 9)
C. y - 3 = three-fifths(x + 6)
D. y + 3 = three-fifths(x – 6)
To determine the equation that represents the line passing through the two points (6, –3) and (–4, –9), we can use the point-slope equation:
\(y - y_1 = \frac{{y_2 - y_1}}{{x_2 - x_1}}(x - x_1)\),
where (x1, y1) and (x2, y2) are the coordinates of the given points.
Using the given points (6, –3) and (–4, –9), we can substitute the corresponding values into the equation and simplify to determine the correct equation.
For point (6, –3):
\(y - (-3) = \frac{{(-9) - (-3)}}{{-4 - 6}}(x - 6)\),
\(y + 3 = \frac{{-9 + 3}}{{-4 - 6}}(x - 6)\),
\(y + 3 = \frac{{-6}}{{-10}}(x - 6)\),
\(y + 3 = \frac{3}{5}(x - 6)\).
For point (–4, –9):
\(y - (-9) = \frac{{(-9) - (-3)}}{{-4 - 6}}(x - (-4))\),
\(y + 9 = \frac{{-6}}{{-10}}(x + 4)\),
\(y + 9 = \frac{3}{5}(x + 4)\).
The equation in the correct form is y + 3 = (3/5)(x - 6).
Therefore, the correct equation that represents the line passing through the two points is:
y + 3 = (3/5)(x - 6).
Hence, the answer is option D.