Question

6. Find the equation of the line that is parallel to the line 6x-3y+18=0 and that passes through the point (2,1). Write your answer in the form of h=mx+c

Answer 1

To find the equation of a line parallel to 6x - 3y + 18 = 0 and passing through the point (2,1), rearrange the equation to y = mx + c, find the slope, plug in the point to solve for c, resulting in y = 2x - 3.

Step-by-step explanation:

To find the equation of a line parallel to 6x - 3y + 18 = 0 and passing through the point (2,1), we need to find the slope of the given line. The equation of a line in the form y = mx + c, where m is the slope, can be used to find the equation of the parallel line.

Step 1: Rearrange the equation 6x - 3y + 18 = 0 to the form y = mx + c. Doing this, we get -3y = -6x - 18, then divide by -3 to get y = 2x + 6.

Step 2: Since the parallel line has the same slope as the given line, the slope is m = 2.

Step 3: Plugging in the point (2,1) into the equation y = 2x + c, we can solve for c. 1 = 2(2) + c, 1 = 4 + c, c = -3.

Therefore, the equation of the line parallel to 6x - 3y + 18 = 0 and passing through the point (2,1) is y = 2x - 3.

Answer 2

y = 2x- 3

Step-by-step explanation:

1) D // D' , this means that mD = mD'

6x -3y +18 =0

6x +18 =3y

6x/3 +18/3 = y

2x +6 = y. m= 2

2) Find the equation of D'

y - y' = m (x - x')

y - 1 = 2(x - 2)

y-1 = 2x - 4

y = 2x-3