Question

Select the correct answer.

If a line crosses the y-axis at (0, 1) and has a slope of `4/5`, what is the equation of the line?

A.
4y − 5x = 5

B.
y − 4x = 5

C.
5y + 4x = 5

D.
5y − 4x = 5

Answer 1

D.

5y − 4x = 5

Step-by-step explanation

The general formula of a line function is;

y = mx + c

Where m is the slope and c is the y-intercept.

From the information given;

m = 4/5

c = 1

y = (4/5)x + 1

5y = 4x + 5

5y - 4x = 5

Answer 2

For this case we have, by definition, the slope-intercept equation of a line given by:

`y = mx + b`

Where:

m is the slope

b is the cut point with the y axis

If we are told that the line crosses the axis and in (0,1), we have that
`b = 1`

In addition, they tell us that
`m = \frac {4} {5}`

Substituting in the generic equation we have:

`y = \frac {4} {5} x + 1`

This is equivalent to:

`y-1 = \frac {4} {5} x`

`5 (y-1) = 4x\\5y-5 = 4x\\5y-4x = 5`

Thus, the equation of the line is:
`5y-4x = 5`

ANswer:

Option D