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Which point lies on the line described by the equation below?

[tex]\[ y + 3 = 2(x - 1) \][/tex]

A. [tex]\((2, 9)\)[/tex]
B. [tex]\((2, 1)\)[/tex]
C. [tex]\((1, -4)\)[/tex]
D. [tex]\((0, 0)\)[/tex]
E. [tex]\((1, -3)\)[/tex]
F. [tex]\((-1, -6)\)[/tex]

Sagot :

GinnyAnswer
To determine which point lies on the line described by the equation [tex]\( y + 3 = 2(x - 1) \)[/tex], we start by converting the given equation into the slope-intercept form, [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.

First, let's rearrange the given equation:

[tex]\[ y + 3 = 2(x - 1) \][/tex]

Distribute the 2 on the right side:

[tex]\[ y + 3 = 2x - 2 \][/tex]

Subtract 3 from both sides to isolate [tex]\( y \)[/tex]:

[tex]\[ y = 2x - 2 - 3 \][/tex]

Simplify the equation:

[tex]\[ y = 2x - 5 \][/tex]

Now we have the line in slope-intercept form: [tex]\( y = 2x - 5 \)[/tex].

Next, we need to check which points satisfy this equation. We will substitute the coordinates of each point into the equation [tex]\( y = 2x - 5 \)[/tex] and see which one holds true.

A. [tex]\((2, 9)\)[/tex]:

Substitute [tex]\( x = 2 \)[/tex] and [tex]\( y = 9 \)[/tex]:

[tex]\[ 9 = 2(2) - 5 \][/tex]
[tex]\[ 9 = 4 - 5 \][/tex]
[tex]\[ 9 = -1 \][/tex]

This is not true.

B. [tex]\((2, 1)\)[/tex]:

Substitute [tex]\( x = 2 \)[/tex] and [tex]\( y = 1 \)[/tex]:

[tex]\[ 1 = 2(2) - 5 \][/tex]
[tex]\[ 1 = 4 - 5 \][/tex]
[tex]\[ 1 = -1 \][/tex]

This is not true.

C. [tex]\((1, -4)\)[/tex]:

Substitute [tex]\( x = 1 \)[/tex] and [tex]\( y = -4 \)[/tex]:

[tex]\[ -4 = 2(1) - 5 \][/tex]
[tex]\[ -4 = 2 - 5 \][/tex]
[tex]\[ -4 = -3 \][/tex]

This is not true.

D. [tex]\((0, 0)\)[/tex]:

Substitute [tex]\( x = 0 \)[/tex] and [tex]\( y = 0 \)[/tex]:

[tex]\[ 0 = 2(0) - 5 \][/tex]
[tex]\[ 0 = 0 - 5 \][/tex]
[tex]\[ 0 = -5 \][/tex]

This is not true.

E. [tex]\((1, -3)\)[/tex]:

Substitute [tex]\( x = 1 \)[/tex] and [tex]\( y = -3 \)[/tex]:

[tex]\[ -3 = 2(1) - 5 \][/tex]
[tex]\[ -3 = 2 - 5 \][/tex]
[tex]\[ -3 = -3 \][/tex]

This is true.

F. [tex]\((-1, -6)\)[/tex]:

Substitute [tex]\( x = -1 \)[/tex] and [tex]\( y = -6 \)[/tex]:

[tex]\[ -6 = 2(-1) - 5 \][/tex]
[tex]\[ -6 = -2 - 5 \][/tex]
[tex]\[ -6 = -7 \][/tex]

This is not true.

Therefore, the point that lies on the line [tex]\( y + 3 = 2(x - 1) \)[/tex] is:

E. [tex]\((1, -3)\)[/tex]
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