Question

What is the equation of the line ?

Answer 1

Answer: OPTION A

Step-by-step 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:

$m=\frac{5-(-3)}{4-(-2)}=\frac{4}{3}$

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

$5=\frac{4}{3}(4)+b\\ b=-\frac{1}{3}$

Then, the equation of the line is:

$y=\frac{4}{3}x-\frac{1}{3}$

Answer 2

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

Step-by-step 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