Write the equation of the line that satisfies the given condition: contains the point (-8, -4) and is parallel to the line x + 4 y = -3. Choose the final equation from the following (the equations are given in standard form).
A) 4 x + y = 8
B) 4 x + y = -8
C) x + 4 y = 8
D) x + 4 y = -3

Question

Quizplus · Accepted Answer

We know that the line we need to find is parallel to x + 4y = -3, which can be rearranged to 4y = -x - 3 or y = -1/4 x - 3/4. Since parallel lines have the same slope, our line must have a slope of -1/4. To find the equation of the line, we can use the point-slope form y - y1 = m(x - x1) and plug in the given point (-8, -4) and slope -1/4. This gives us y + 4 = -1/4(x + 8). Rearranging and putting into standard form gives us x + 4y = 8, which is choice C.

Write the Equation of the Line That Satisfies the Given