Question

What is the equation of the line which includes points HELP ASAP

Answer 1

Answer:

OPTION C

OPTION A

OPTION C

Step-by-step explanation:

We use two - point form to determine the equation of the line when two points are given.

The two - point form is: $\frac{y - y_1}{y_2 - y_1} = \frac{x - x_1}{x_2 - x_1}$, where $(x_1, y_1)$ and $(x_2, y_2)$ are the two points passing through it.

1) (x₁, y₁) = (2, 3) and (x₂, y₂) = (0, 10)

Using the two - point form, we have:

$\frac{y - 3}{10 - 3} = \frac{x - 2}{0 - 2}$

$\frac{y - 3}{7} = \frac{x -2}{-2}$

$\implies - 2y + 6 = 7x - 14$

$\implies 7x - 20 = - 2y$

Dividing by -2, we get:

$y = - \frac{7}{2}x + 10$ is the equation of the line.

2) (x₁, y₁) = (1, 1) and (x₂, y₂) = (1, 5)

Using the slope - point form, we get:

$\frac{y - 1}{5 - 1} = \frac{x - 1}{1 - 1}$

$\implies \frac{y - 1}{5 - 1} = \frac{x - 1}{0}$

$0 = x - 1$

⇒ x = 1 is the required equation of the line.

3) (x₁, y₁) = (-5, 5) and (x₂, y₂) = (2, 5)

Using the slope - point form, we get:

$\frac{y - 5}{5 - 5} = \frac{x + 5}{2 - 5}$

$\implies \frac{y - 5}{0} = \frac{x + 5}{-3}$

$\implies y - 5 = 0$

⇒ y = 5 is the required equation of the line.