Question

Write the slope intercept form of the equation of the line passing through the point (5, -4) and perpendicular to the line y=-4/3x+5

Answer 1

Y = -4/3x + 5....the slope here is -4/3. A perpendicular line will have a negative reciprocal slope. To find the negative reciprocal, flip the original slope and change the sign. So we have -4/3....we flip it and it becomes - 3/4....we change the sign and it becomes 3/4. So the perpendicular line will have a slope of 3/4.

y = mx + b
slope(m) = 3/4
(5,-4)...x = 5 and y = -4
now we sub into the formula and find b, the y int
-4 = 3/4(5) + b
-4 = 15/4 + b
-4 - 15/4 = b
-16/4 - 15/4 = b
-31/4 = b
so ur perpendicular equation is : y = 3/4x + (-31/4) which is written as :
 y = 3/4x - 13/4 <== ur answer

Answer 2

As this line is perpendicular to the line y=-4/3x+5 , so it has une equation: y=3/4x+b, b is unknown. ( you know that a*a'=-1)
IN addition, this line pass through the point (5;-4) and we have x=5 and y=-4
so, -4=3/4 x 5 +b and b=-4-15/4=-31/4
And we have y=3/4x-31/4
Have fun