(-2,6); perpendicular to y=-5/4-3

Question

write an equation for the line in slope intercept form

Answer 1

y= -5x/4 - 3

slope = negative inverse

y= 4x/5 + b

plug in the point (-2,6)

6= (4/5)(-2) +b

where b= y intercept

b = 6+8/5= 38/5

y= 4x/5 + 38/5

Answer 2

If you mean perpendicular to the equation y = -5/4x - 3 (you didn't put in the "x"), then the slope of that line is -5/4. The perpendicular to that would have a slope of 4/5 (the negative reciprocal).

Using the point-slope form of a line (y - y₁) = m(x - x₁) where m = 4/5 and (x₁, y₁) is (-2, 6) then:

(y - 6) = 4/5(x - -2)

y - 6 = 4/5(x + 2)

y - 6 = 4/5x + 8/5

y = 4/5x + 8/5 + 6

y = 4/5x + 8/5 + 30/5

y = 4/5x + 38/5