Question

Find the equation of a line with x-intercept 5 and passing through the point (−2, 3).

Answer 1

Given:

An x-intercept of 5 means the line crosses the x-axis at the point (5, 0),

The second point provided is (−2, 3),

Using the slope formula:

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

Substituting (x₁, y₁) = (5, 0) and (x₂, y₂) = (−2, 3),

m = `(3 - 0)/(-2 - 5)`

= `3/-7`

∴ m = `-3/7`

Using the point–slope formula with the point (5, 0):

y − y₁ = m(x − x₁)

`y - 0 = -3/7 (x - 5)`

7y = −3(x − 5)

7y = −3x + 15

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

3x + 7y − 15 = 0

Hence, the equation of a line is 3x + 7y − 15 = 0.