Question

What is the equation of the line ?

Answer 1

Answer:Tthe correct answer is option A. y = 4x/3 - 1/3

Explanation:

From the given figure we get two points of the line.

(4,5) and (-2,-3)

To find the slope of line

slope m = (y₂ - y₁)/(x₂ - x₁)

(x₁,y₁) = (-2,-3)

(x₂,y₂) = (4, 5)

m = (y₂ - y₁)/(x₂ - x₁) =(5 - -3) (4 - -2) = 8/6 = 4/3

To find the equation

The equation is given by,

(y - y₁) = m(x - x₁)

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

y + 3 = 4(x+2)/3

3y + 9 = 4x + 8

3y = 4x - 1

y = 4x/3 - 1/3

Therefore the correct answer is option A. y = 4x/3 - 1/3

Answer 2

Answer: OPTION A

Explanation:

The equation of the line, by definition, has the following form:

y=mx+b

Where m is the slope and b is the y-intercept.

Calculate the slope as following:

`m=(5-(-3))/(4-(-2))=(4)/(3)`

Now, you must solve for the y-intercept, as you can see below:

`5=(4)/(3)(4)+b\\ b=-(1)/(3)`

Then, the equation of the line is:

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