Question

Given the equation y = 4/3x + 7, write the equation of a line through (-6,10) that is parallel to the line given above. What is the equation of the parallel line?

a) y = 4/3x - 10
b) y = -4/3x - 7
c) y = 3/4x + 10
d) y = -3/4x - 10

Answer 1

To find the equation of a line parallel to y = 4/3x + 7 and passing through (-6,10), we write the equation using the point-slope form. The equation of the parallel line is y = (4/3)x + 18.

Step-by-step explanation:

To find the equation of a line parallel to y = 4/3x + 7, we use the fact that parallel lines have the same slope. The given line has a slope of 4/3, so the parallel line will also have a slope of 4/3. Since the line passes through the point (-6,10), we can use the point-slope form of a linear equation to find the equation of the line:

y - y1 = m(x - x1)

Substituting the values into the equation, we get:

y - 10 = (4/3)(x - (-6))

y - 10 = (4/3)(x + 6)

y - 10 = (4/3)x + 8

y = (4/3)x + 8 + 10

y = (4/3)x + 18

Therefore, the equation of the line parallel to y = 4/3x + 7 and passing through (-6,10) is y = (4/3)x + 18, which corresponds to answer choice d).