Question

Which is the equation of a line that is parallel to 2x + 5y = 4 and goes through the point (5, –4) ?

A. y=-2/5x-6
B. y=-2/5x+2
C. y=2/5x-6
D. y=-2/5x-2

Answer 1

`y = (-2)/(5) x - 2`

Step-by-step explanation:

The general formula of the linear equation is:

y = mx + c where m is the slope and c is the y-intercept

1- getting the slope of the given line:

The given line is:

2x + 5y = 4

Rearrange to be in the general formula:

5y = -2x + 4 .............> y =
`(-2)/(5) x + 4`

slope of the given line is :
`(-2)/(5)`

2- getting the slope of the required line:

We are given that the two lines are parallel, this means that they have equal slopes.

Therefore:

slope of the required line =
`(-2)/(5)`

The equation of the required line now became : y =
`(-2)/(5)`x + c

3- getting the value of c:

We are given that the line passes through the point (5,-4). This means that this point satisfies the equation of the line.

Therefore, we will substitute with the point in the equation and solve for c as follows:

y =
`(-2)/(5)`x + c

-4 =
`(-2)/(5)` (5) + c

-4 = -2 + c

c = -4 + 2

c = -2

Based on the above, the equation of the line is:

`y = (-2)/(5) x - 2`

Hope this helps :)

Answer 2

we know that

if two lines are parallel

then

their slopes are equal

Step 1

Find the slope of the line 2x + 5y = 4

2x + 5y = 4------> 5y=4-2x-----> y=(4/5)-(2/5)x------> slope m=(-2/5)

step 2

with m=-2/5 and the point (5, –4) find the equation of the line

y-y1=m*(x-x1)------> y+4=(-2/5)*(x-5)----> y=(-2/5)x+2-4

y=(-2/5)x-2

therefore

the answer is the option D