perpendicular 3x+6y=12 — step-by-step solution

⇥1) Let's solve in

ℝ

3 x + 6 y = 12

⇥

6 y = 12 - 3 x

⇥ⓘ Both sides are divided by

6

⇥

y = \frac{12 - 3 x}{6}

⇥ⓘ A fraction is simplified by dividing the numerator and the denominator by the same number:

\frac{12 - 3 x}{6}

\frac{4 - x}{2}

⇥Solution obtained:

y = \frac{4 - x}{2}

The slope-intercept form is

y = m x + b

: the slope is

- \frac{1}{2}

and the y-intercept is

2

No point is specified: find the family of perpendicular lines

m

is the slope of the perpendicular line. The slopes of two perpendicular lines have product -1:

- \frac{1}{2} \cdot m = -1

⇥2) Let's solve in

ℝ

- \frac{1}{2} \cdot m = -1

⇥ⓘ Multiplying a fraction by a term multiplies its numerator:

- \frac{1}{2} \cdot m

- \frac{1 \cdot m}{2}

- \frac{m}{2}

⇥

- \frac{m}{2} = -1

⇥

- m = -1 \cdot 2

⇥ⓘ A single minus sign does not cancel out, the product of a negative number by a positive number is negative:

-1 \cdot 2

-2

⇥

- m = -2

⇥Solution obtained:

m = 2

The y-intercept

b

is an arbitrary real number

▶Perpendicular lines:

y = 2 x + b