Question

Line L1represents the graph of 3x+4y=-14. Line L2 passes through the point (-5,7), and is perpendicular to line L1. Write the equation of line L2 in the form y=mx+b

Answer 1

Y = 4/3x + 41/3 is the answer

Answer 2

y =
`(4)/(3) x` +
`(41)/(3)`

Explanation:

1. We are given an equation however lets rearrange it to make sense of it

3x +4y = -14

4y = - 3x - 14

y = - 3/4 x - 14/4

2. Now we can tell our gradient is -3/4 we are told that the other line is perpendicular to this line so since we know the product of the gradients of perpendicular lines = -1 we can take the negative reciprocal of it which would be 4/3 which would be perpendicular to L1

3. We are told this new line passes through the point (-5,7) so we can input those co-ordinates to find the rest of the equation

7 = 4/3 x (-5) + c =

7 = -20/3 + c =

7 +20/3 = c =

21/3 +20/3 = c =

41/3 = c or 13 2/3 = c

so the answer to your question is

y =
`(4)/(3) x` +
`(41)/(3)`