Question

A particle moves from coordinates (0, 3) to coordinates (1, 8). Assuming that the path of the particle is linear, what is the equation of the path?

Answer 1

ANSWER


`y = 5x + 3`

EXPLANATION

If particle moves from coordinates (0, 3) to coordinates (1, 8) and it traces a linear path, then its equation can be obtained using the formula;


`y=mx + c`

We calculate the slope of this line using


`m = (y_2-y_1)/(x_2-x_1)`


`m = (8 - 3)/(1 - 0) = 5`

The point (0,3) is the y-intercept of the line, hence c=3.

The equation of the line is therefore;


`y = 5x + 3`

Answer 2

The equation of the path

y = 5x + 3

Explanation:

It is given that, a particle moves from coordinates (0, 3) to coordinates (1, 8).

To find the slope

Slope = (y₂ - y₁)/(x₂ - x₁)

= (8 - 5)/(1 - 0) = 5

To find the equation of line

Let (x₁, y₁) = (0, 3)

(y - y₁)/(x - x₁) = 5

(y - 3)/(x - 0) = 5

(y - 3)/x = 5

y - 3 = 5x

y = 5x + 3