Answered

Discover the best answers at Westonci.ca, where experts share their insights and knowledge with you. Connect with a community of experts ready to provide precise solutions to your questions quickly and accurately. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

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]
Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.