Question

Find the equation of the line that is parallel to the line x + 5y = 10 and passes through the point (1,3).

Answer 1

Answer:

Step-by-step explanation:

for two lines to be parallel they MUST have the same slope but have different Y intercepts ( Y axis crossing values)

parallel lines will never intersect each other

first I use a graphing calcuator to solve the problem

I like to use y intercept form better, but you don't have use it

I will try to solve it directly without going through the y intercept equation

x + 5y = 10    in y intercept form y = mx + b is

5y = -x + 10     divide both sides by 5

y = -x/5 + 10/5    

y = -x/5 + 2

Now I need to find a parallel line that passes through the x =1 and y = 3 point recall this line will have the same slope =     m = -1/5

and a different Y axis crossing point 'b' that we don't know

y = -x/5 + b      y = 3 when x = 1 so slove for 'b'

3 = -1/5 + b

3 = -0.2 + b    add -0.2 to both sides

3.2 = b

y = -x/5 + 3.2     this is answer in y intercept form

                          if you multiply both sides by 5

5y = -x + 16        add x to both sides

x + 5y = 16         answer in standard form

THE EASIER WAY TO SOLVE THE PROBLEM IS ......

x + 5y = 10      find a line parallel that passes through x  = 1,  y = 3  

x + 5y = Z       Z is an unknown value  plug in x and y and solve for Z

1 + 5(3) = Z

Z = 16              so the parallel line in standard form is

x + 5y = 16    

same as before,  my y intercept method was correct, but not  worth the effort