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If a point lies on a line, then the coordinates of the point must satisfy the equation of the line

y = 2x - 8

I. P(3,-2)
RHS: 2(3) - 8 = -2
LHS: -2
=> Yes

II. P(-8,0)
RHS: -24
LHS: 0
=> No

III. P(1/2,-7)
RHS: -7
LHS: -7
=> Yes

Answer: D
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y = 2*x - 8
points must satisfy the equation if it lies on the respective line
1. (3, -2) ;
-2 = 3*2 - 8
-2 = 6-8
-2 = -2 (Yes)

2. (-8 , 0)
0 = 2*-8 - 8
No

3. (1/2 , -7)
-7 = 2(1/2) - 8
-7 = -7
Yes

Only (1) & (3) satisfy the equation.
Answer: D
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Bunuel
Which of the following points in the coordinate plane lies on the line y = 2x – 8?

I. \((3, -2)\)
II. \((-8, 0)\)
III. \((\frac{1}{2}, -7)\)

(A) I only
(B) III only
(C) I and II only
(D) I and III only
(E) I, II, and III

Solution:

If a point (a, b) lies on the line y = 2x - 8, then b = 2a - 8. Now, let’s check which of the given coordinates satisfies the equation:

I. -2 = 2(3) - 8 ?

-2 = -2 ? → Yes

II. 0 = 2(-8) - 8 ?

0 = -24 ? → No

III. -7 = 2(1/2) - 8

-7 = -7 ? → Yes

Answer: D
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Approach:

Substitute values in the equation y = 2x - 8.

Only I and III satisfies.

Option D
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