Question

Which of the following equation(s) are equivalent to y − 4 = 2/3(x − 1)?

A y= 2/3x - 10/3
B y= 2/3x - 3 1/3
C y= 2/3x + 3
D y= 2/3 + 10/3

Answer 1

• D) y = 2/3x + 10/3

Explanation:

Given

Equation of the line in point-slope form:

• y - 4 = 2/3(x - 1)

Convert the equation into slope-intercept form of y = mx + b:

• y - 4 = 2/3(x - 1)
• y - 4 = 2/3x - 2/3
• y = 2.3x + 4 - 2/3
• y = 2/3x + (12 - 2)/3
• y = 2/3x + 10/3

Correct choice is D

Answer 2

`\textsf{D.} \quad y=(2)/(3)x+(10)/(3)`

Explanation:

Given equation:

`y-4=(2)/(3)(x-1)`

Distribute the parentheses on the right side of the equation:

`\implies y-4=(2)/(3)x-(2)/(3)`

Add 4 to both sides:

`\implies y-4+4=(2)/(3)x-(2)/(3)+4`

`\implies y=(2)/(3)x-(2)/(3)+4`

Rewrite 4 as 12/3:

`\implies y=(2)/(3)x-(2)/(3)+(12)/(3)`

`\implies y=(2)/(3)x+(12)/(3)-(2)/(3)`

`\textsf{Apply the fraction rule} \quad (a)/(c)-(b)/(c)=(a-b)/(c):`

`\implies y=(2)/(3)x+(12-2)/(3)`

`\implies y=(2)/(3)x+(10)/(3)`

Therefore, the equation that is equivalent to the given equation is:

`\boxed{y=(2)/(3)x+(10)/(3)}`