What is the equation of a line that is parallel to the line 2x+5y=10 and passes through the point (-5,1)? check all that apply.

y=-2/5 x -1 (It says check all that apply... I hope this equation hasn't been written in a different form in your choices-let me know)

Step-by-step explanation:

Rearrange 2x+5y=10 into slope-intercept form.

First step: Subtract 2x on both sides:  5y=-2x+10

Second step: Divide both sides by 5 giving: y=-2/5 x+2

The slope is -2/5.

Parallel lines have the same slope.

So we know the equation of our new line is in the form y=-2/5 x+b.

We need to find the y-intercept of our line... let's just use the point they have our line going through to find it. Plug in and solve for b.

1=-2/5 (-5)+b

1=2+b

-1=b

So the equation is y=-2/5 x -1

see explanation

Step-by-step explanation:

The equation of a line in slope- intercept form is

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

Rearrange 2x + 5y = 10 into this form

Subtract 2x from both sides

5y = - 2x + 10 ( divide all terms by 5 )

y = - x + 2 ← in slope- intercept form

with slope m = -

• Parallel lines have equal slopes, so

y = - x + c ← is the partial equation of the parallel line

To find c substitute (- 5, 1) into the partial equation

1 = 2 + c ⇒ c = 1 - 2 = - 1

y = - x - 1 ← in slope- intercept form

Multiply through by 5

5y = - 2x - 5 ( add 2x to both sides )

2x + 5y = - 5 ← in standard form