Provide an appropriate response.
-Write the equation of a line that passes through (3, 9) and (0, -7). Write the final answer in the form Ax + By = C where A, B, and C are integers with no common divisors (other than ±1) and A 0.
A) 16x - 3y = -21
B) 16x - 3y = 21
C) -16x + 3y = 21
D) 3x - 16y = 21

Question

Provide an appropriate response.
-Write the equation of a line that passes through (3, 9) and (0, -7). Write the final answer in the form Ax + By = C where A, B, and C are integers with no common divisors (other than ±1) and A > 0.
A) 16x - 3y = -21
B) 16x - 3y = 21
C) -16x + 3y = 21
D) 3x - 16y = 21

Quizplus · Accepted Answer

First, find the slope (m) using the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$, which gives $m = \frac{-7 - 9}{0 - 3} = \frac{-16}{-3} = \frac{16}{3}$. Then, use point-slope form (y - y1 = m(x - x1)) with one of the points, say (3, 9), to get $y - 9 = \frac{16}{3}(x - 3)$. Simplify and rearrange to get $16x - 3y = 21$, which matches option B.

Provide an Appropriate Response