How to find the equation.?

Question

1. Write an equation of a line containing the point (-3,5) if it's graph had no y intercept

2. Write an equation of a line x int - 4 y int 5.

Answer 1

(1).

The point is (-3, 5) and the line does not contain y-intercept that means the line passes through point origin.

Two-points form of line equation: y - y₁ = [(y₂ - y₁)/(x₂ - x₁)] (x - x₁), where (x₁, y₁) and (x₂, y₂) are two pints.

Substitute (x₁, y₁) = (-3, 5) and (x₂, y₂) = (0, 0) in the two-points form of line equation.

y - 5 = [(0 - 5)/(0 + 3)] (x + 3)

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

3(y - 5) = -5(x + 3)

3y - 15 = - 5x - 15

3y = - 5x

y = (- 5/3)x.

The line equation is y = (- 5/3)x.

Graph:

Answer 2

(2).

The x-intercept of the line is -4 and its y-intercept is 5.

Intercept form of line equation: x/a + y/b = 1, a = x-intercept and b = y-intercept.

Substitute a = -4 and b = 5 in the intercept form of line equation.

x/(-4) + y/5 = 1

5x - 4y = - 20

The line equation is 5x - 4y = - 20.