Answer:
The equation x + 2y = -1 describes a line with a slope of -1/2 that contains the point (-5, 2) ⇒ D
Step-by-step explanation:
Let us use this rule to solve the question
The slope of the line is [tex]-\frac{1}{2}[/tex] 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 = [tex]\frac{-1}{2}[/tex]
∴ 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 = [tex]\frac{-1}{-2}[/tex] = [tex]\frac{1}{2}[/tex]
∴ 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 = [tex]\frac{-1}{-2}[/tex] = [tex]\frac{1}{2}[/tex]
∴ 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 = [tex]\frac{-1}{2}[/tex]
∴ 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)
