perpendicular 2x+5y=10 — step-by-step solution

⇥Let's solve in

ℝ

2 x + 5 y = 10

⇥

5 y = 10 - 2 x

⇥Solution obtained:

y = \frac{10 - 2 x}{5}

The slope-intercept form is

y = m x + b

: the slope is

- \frac{2}{5}

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{2}{5} \cdot m = -1

⇥Let's solve in

ℝ

- \frac{2}{5} \cdot m = -1

⇥

- \frac{2 m}{5} = -1

⇥

- 2 m = -1 \cdot 5

⇥

- 2 m = -5

⇥

2 m = 5

⇥Solution found:

m = \frac{5}{2}

The y-intercept

b

is an arbitrary real number

▶Perpendicular lines:

y = \frac{5 x}{2} + b