Question

Which equations represent the line that is parallel to 3x – 4y = 7 and passes through the point (-4,-2)? Select two options.

a. y = (3/4)x + 1
b. 3x - 4y = -4
c. 4x – 3y = -3
d. y - 2 = -(3/4)(x - 4)
e. y + 2 = 2(x + 4)

Answer 1

To find the equation of a line that is parallel to 3x – 4y = 7 and passes through the point (-4,-2), rearrange the original equation to get y = (3/4)x - 7/4. The slope of the original line is 3/4. Parallel lines have the same slope, so the equation of the line parallel to 3x – 4y = 7 is y = (3/4)x + b. The values of b can be found by plugging in the given coordinates.

Step-by-step explanation:

To find the equation of a line that is parallel to 3x – 4y = 7 and passes through the point (-4,-2), we need to find the slope of the original line and use it to write the equation of the parallel line.

Rearranging the original equation, we get y = (3/4)x - 7/4, which means the slope of the original line is 3/4.

Since parallel lines have the same slope, the equation of the line parallel to 3x – 4y = 7 is y = (3/4)x + b.

Plugging in the coordinates of the given point, we can solve for b. -2 = (3/4)(-4) + b, which gives us b = 1.

Therefore, two equations that represent the line parallel to 3x – 4y = 7 and passes through the point (-4,-2) are y = (3/4)x + 1 and y - 2 = -(3/4)(x - 4).