Find an equation for the line that passes through the given point and satisfies the given conditions.
-P = (-8, -3); parallel to v = -3i + 7j
A) y + 3 = 2(x + 3)
B) -3x + 7y = 3
C) 7x + 3y = -65
D) -3x + 7y = 58

Question

Quizplus · Accepted Answer

The slope of the line parallel to vector v = -3i + 7j is given by the ratio of the j-component to the i-component, which is -(-3)/7 = 3/7. Using the point-slope form of a line, y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point (-8, -3), we get y + 3 = (3/7)(x + 8). Multiplying both sides by 7 to clear the fraction gives 7y + 21 = 3x + 24, or 7y = 3x + 3. Rearranging to standard form, we get 7x + 3y = -65, which matches option C.

Find an Equation for the Line That Passes Through the Given