Question

4.

3. Consider the line
2x + 5y = -10. What is the
slope of the line parallel to this line?

Answer 1

The slope of the parallel line to the line 2x + 5y = -10 is
`-(2)/(5)`

Explanation:

Parallel lines have equal slopes and different y-intercepts

To find the slope of the line from the equation of the line, then put the equation in the form y = m x + b, where

• m is the slope

• b is the y-intercept

Let us solve the question

∵ The equation of a line is 2x + 5y = -10

→ Put the equation in the form above

→ Subtract x from both sides to move 2x from the left side to the

right side

∴ 2x - 2x + 5y = -10 - 2x

∴ 5y = -10x - 2x

→ Make the coefficient of y equal 1 by dividing all terms by 5

∵
`(5y)/(5)=-(10)/(5)-(2x)/(5)`

∴ y = -2 -
`(2)/(5)x`

→ Compare it by the form of the equation above

∴ m =
`-(2)/(5)`

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

→ We need the slope of the line which is parallel to the given line

∵ Parallel lines have the same slopes

∴ The slope of the parallel line to the line 2x + 5y = -10 is
`-(2)/(5)`