Question

A line passes through (3,-2) and (6, 2). Write an equation for the line in point-slope form.

Answer 1

Answer:

see explanation

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (3, - 2) and (x₂, y₂ ) = (6, 2)

m = $\frac{2+2}{6-3}$ = $\frac{4}{3}$

Use either of the 2 points as the point on the line

Using (a, b) = (6, 2), then

y - 2 = $\frac{4}{3}$(x - 6) ← in point- slope form

The equation of a line in standard form is

Ax + By = C ( A is a positive integer and B, C are integers )

Multiply both sides of the point- slope equation by 3

3y - 6 = 4(x - 6) ← distribute

3y - 6 = 4x - 24 ( subtract 3y from both sides )

- 6 = 4x - 3y - 24 ( add 24 to both sides )

18 = 4x - 3y, that is

4x - 3y = 18 ← in standard form

Answer 2

Answer:

(y - -2) (6 - 3) - (2 - -2) (x - 3) = 0

6y + 2 - 3y - 6 -2x +6 +2x +6 = 0

3y +8 =0

3y = -8

y = -8/3

Step-by-step explanation: