contestada

What is the equation in point−slope form of the line passing through (0, 6) and (1, 3)?

A. (y − 3) = −3(x − 1)

B. (y + 3) = 3(x + 1)

C. (y + 3) = −3(x + 1)

D. (y − 3) = 3(x + 6)

Respuesta :

a is the correct answer. slope is 6-3/0-1=3/-1=-3
so y-3 =-3(x-1)

Answer:

A. [tex](y-3)=-3(x-1)[/tex]

Step-by-step explanation:

We have been given coordinates of two points (0, 6) and (1, 3). We are asked o find the equation of line passing through the given points in point- slope form.

We know that the point-slope form of equation is in format: [tex](y-y_1)=m(x-x_1)[/tex], where,

[tex]m=\text{Slope of line}[/tex],

[tex](x_1,y_1)=\text{Coordinates of a point on line}[/tex]

First of all, we will find the slope of line using coordinates of given point in slope formula as shown below:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\frac{3-6}{1-0}[/tex]

[tex]m=\frac{-3}{1}[/tex]

[tex]m=-3[/tex]

Upon substituting [tex]m=-3[/tex] and coordinates of point (1, 3) in point-slope form of equation we will get,

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

Therefore, option A is the correct choice.

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