Write an equation for the line parallel to y = − 5/7 x + 16 that passes through the point ( 6 , 6 ) . You may write the equation using any form.

Question

Could someone explain this to me step by step?

Answer 1

Parallel lines have the same slope. So the slope of the new line must be -5/7. But the new line must pass through the point (6,6). There are two formulas you can use to determine the equation of the new line.

One is point-slope:

y - y₁= m (x - x₁) where x₁=6 and y₁=6. Of course m = -5/7

y - 6 =( -5/7) (x - 6)

One way to simplify this is to multiply both sides by 7, realizing the 7 (-5/7) = -5

7y - 42 = -5(x - 6)

7y - 42 = -5x+30

7y = -5x + 72

y = (-5/7)x + 72/7

Or you can distribute the - 5/7 first:

y - 6 = (-5/7)x +30/7

y = (-5/7)x + 30/7 + 6

y = (-5/7) x + 30/7 + 42/7

y = (-5/7)x + 72/7

Or you can use the formula (slope-intercept):

y = mx +b, where we know when x = 6, y = 6 and m = -5/7. Use that info to solve for b.

6 = (-5/7)6 + b

6 = -30/7 + b

b = 42/7 + 30/7

b = 72/7

So the equation is:

y = (-5/7)x + 72/7

Visit here to see the graph of the lines (along with a line perpendicular to the original line and passing through (6,6).

desmos.com/calculator/cxlsomuynb

To visit the above graph select the URL, right-click, and choose Go to...