Respuesta :
Answer:
x + 3y - 9 = 0
Step-by-step explanation:
(d): x + 3y = 15 -> (d): x + 3y - 15 =0
if (d')║(d)
-> (d'): x + 3y + c = 0
but (d') passes through the point (6;1) => c = -x-3y = -6-3.1 = -9
=> (d'): x + 3y - 9 =0
The equation of the line that passes through the point (6,1) and is parallel to the line (x + 3y = 15) is 3y +x = 9 and this can be determined by using the one-point slope form of the line.
Given :
The line passes through the point (6,1) and is parallel to the line (x + 3y = 15).
The following steps can be used in order to determine the equation of the line that passes through the point (6,1) and is parallel to the line (x + 3y = 15):
Step 1 - Remember that when two lines are parallel then their slopes are equal.
Step 2 - So, the slope of the line that passes through the point (6,1) is -1/3.
Step 3 - So, using the one-point slope form of a line the equation of a line that passes through the point (6,1) and is parallel to the line (x + 3y = 15) can be determined.
Step 4 - The one-point slope form is given below:
[tex](y-y_1)=m(x-x_1)[/tex]
Step 5 - Substitute the values of the known terms in the above equation.
[tex](y-1)=-\dfrac{1}{3}(x-6)[/tex]
3y - 3 = -x + 6
3y +x = 9
For more information, refer to the link given below:
https://brainly.com/question/2564656
