Question

Find an equation of the line that (a) has y-intercept of 7 and (b) is parallel to the line -5x-6y=1

Write your answer in the form y=mx+b

Answer 1

6y = -5x + 42

Explanation:

-5x - 6y = 1

-6y = 5x + 1---------------------(i)

y = -5x/6 - 1/6

comparing the equation above with y = mx + c, we have;

m = -5/6

for condition of parallelism

the gradient of the new line = -5/6

Using the formula

y = mx + c

y = -5x/6 + 7

6y = -5x + 42

Answer 2

The answer to your question is 5x + 6y - 42 = 0

Explanation:

Data

y-intercept = 7

parallel to -5x - 6y = 1

Process

1.- Find the slope

- 6y = 5x + 1

y = -5/6 x - 1/6

As the lines are parallels, the slope is the same in both lines

m = -5/6

2.- Find the equation of the new line

If the line has a y-intercept of 7, it means that the point is (0, 7)

y - y1 = m(x - x1)

Substitution

y - 7 = -5/6 (x - 0)

Simplification

y - 7 = -5/6x

Equal to zero

5/6x + y - 7 = 0

Multiply by 6

5x + 6y - 42 = 0 This is the equation of the line