Question

Which equation describes a line with a slope of -1/2 that contains the point (-5, 2)?

A. x + 2y = 1
B. x - 2y = -1
C. x - 2y = 1
D. x + 2y = -1

Answer 1

The equation x + 2y = -1 describes a line with a slope of -1/2 that contains the point (-5, 2) ⇒ D

Explanation:

• The slope of the linear equation of the form ax + by = c is m =
  `(-a)/(b)` , where a and b are integers

Let us use this rule to solve the question

The slope of the line is
`-(1)/(2)` and the line contains the point (-5, 2)

We want to find which equation has the same slope and contains the point

A.

∵ x + 2y = 1

∴ a = 1 and b = 2

→ Use the rule above to find m

∴ m =
`(-1)/(2)`

∴ The line has the same slope

→ Let us find if the line contains the point (-5, 2), by substituting x by -5

and y by 2 in the left side of the equation if the answer equals

the right side, then the line contains it

∵ L.S = -5 + 2(2) = -5 + 4 = -1

∵ R.S = 1

∴ L.S ≠ R.S

∴ The line does not contain the point (-5, 2)

B.

∵ x - 2y = -1

∴ a = 1 and b = -2

→ Use the rule above to find m

∴ m =
`(-1)/(-2)` =
`(1)/(2)`

∴ The line does not have the same slope

C.

∵ x - 2y = 1

∴ a = 1 and b = -2

→ Use the rule above to find m

∴ m =
`(-1)/(-2)` =
`(1)/(2)`

∴ The line does not have the same slope

D.

∵ x + 2y = -1

∴ a = 1 and b = 2

→ Use the rule above to find m

∴ m =
`(-1)/(2)`

∴ The line has the same slope

→ Substitute x by -5 and y by 2 in the left side

∵ L.S = -5 + 2(2) = -5 + 4 = -1

∵ R.S = -1

∴ L.S = R.S

∴ The line contains the point (-5, 2)

The equation x + 2y = -1 describes a line with a slope of -1/2 that contains the point (-5, 2)