Algebra question

Question

Write in standard form a line with a slope of -2/3 and passes through the origin.

Answer 1

The standard form of a line is

Ax + By = C

We are given the slope m = -2/3

and that the line goes through the

origin (0,0).

Use the point-slope formula

y - y₁ = m (x - x₁)

where (x_1,y₁) is a point

on the line.

Here, we can use (0,0) for (x₁,y₁)

and m = -2/3

Plug in to point-slope formula:

y - y₁ = m (x - x₁)

y - 0 = (-2/3)(x - 0)

y = (-2/3)(x)

y = (-2/3)x

Multiply both sides by 3 to

get rid of the fraction.

3*y = 3*(-2/3)x

3y = -2x

add 2x to both sides to get in

Ax + By = C form

3y + 2x = -2x + 2x

2x +3y = 0

(A=2, B=3, C=0 in this example)

This is the standard

form of a line with

slope = -2/3 going

through the origin

(0,0).

Answer 2