Question

Write an equation for a line that is parallel to 2x+5y=15 and passes through the point (-10, 3)​

Answer 1

the equation of a parallel line is : y=-2/5 x -1

Explanation:

2x+5y=15

put the equation in the form of y=mx+b

2x+5y=15

5y=15-2x

y=15/5-2/5 x

y=-2/5 x+3

parallel lines has the same slope : m=-2/5

passes through point (-10,3) find b

y=-2/5 x +b

3=-2/5(-10)+b

3=20/5 +b

3=4+b

b=3-4

b=-1

the equation of a parallel line is : y=-2/5 x -1

Answer 2

The equation of the line is,

`y = - (2)/(5) x - 1`

Explanation:

First, you have to write it in a form of y = mx + b :

`2x + 5y = 15`

`5y = 15 - 2x`

`y = 3 - (2)/(5) x`

`y = - (2)/(3) x + 5`

When both lines are parallel to each other, they will have to same gradient value. So the equation of the line is y = (-2/5)x + b. Next, you have to find the value of b by substutituting (-10,3) into the equation :

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

`let \: x = - 10,y = 3`

`3 = - (2)/(5) ( - 10) + b`

`3 = 4 + b`

`3 - 4 = b`

`b = - 1`