Question

What is the equation of a line that passes through the point (10, 5) and is perpendicular to the line whose equation is y=5/4 x-2?

Answer 1

Hey there :)

$y = \frac{5}{4}x - 2$
Slope is the coefficient of x ⇒ $\frac{5}{4}$

If the second line is perpendicular to the given line, then the slope of the 2nd line is the reverse/reciprocal of the 1st line ⇒ $\frac{4}{5}$

(10, 5)
  ↑  ↑
  x₁ y₁

Point-slope form is ( y - y₁ ) = m ( x - x₁ )

y - 4 = $\frac{4}{5}$ ( x - 10 )
y - 4 = $\frac{4}{5} x$ - 8

y = $\frac{4}{5} x - 4$ ⇔ The equation of the line that passes through the point (10,5) ans perpendicular to the given line

Answer 2

Answer:

Question with point (10,5)

y=-4/5x+13

Slope of the perpendicular line would be the NEGATIVE reciprical!

Step-by-step explanation:

The answer above is good (except for forgetting it is the negative reciprical) and the person used the point (10,4) not (10,5) from the question...