Question

Find the equations of the line passing through the points (0, −3) and (5, 0).

Answer 1

Given values:

Point A(x₁, y₁) = (0, −3),

Point B(x₂, y₂) = (5, 0),

The slope of a line passing through two points (x₁, y₁) and (x₂, y₂):

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

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

`m = 3/5`

Both the given points are the intercepts:

⇒ Y-intercept (c): The line passes through (0, −3), the Y-intercept is −3.

⇒ X-intercept (a): The line passes through (5, 0), the X-intercept is 5.

Using the Two-Intercept formula `x/a + y/b = 1`:

`x/5 + y/(-3) = 1`

Let’s write the above equation in standard form (Ax + By + C = 0),

3x − 5y = 15    ...[Multiplying by the common denominator, which is 15.]

∴ 3x − 5y − 15 = 0

Hence, the equation of the line is 3x − 5y − 15 = 0.