Question

Equation of a line through 4,6 perpendicular to -5x+4y=4

Answer 1

Answer: y =-(4/5)x + 46/5

Explanation:

To find this, we first need to find the slope of the given equation. We can do this by rearranging it to be in slope-intercept form which is y = mx + b. Start isolating y. -5x = 4 - 4y. -5x - 4 = -4y. -5x/-4 - 4/-4 = y. (5/4)x + 1 = y. This means the slope of the given equation -5x+4y=4 is 5/4. Now, if we want to find the equation of a line perpendicular to this equation we need to take the negative reciprocal of 5/4. This is -4/5. Since we want the line to be through (4,6) we can set up our equation using point slope form. Remember, this is (y-y1)= m(x-x1). So, our equation is y-6 = -4/5(x-4). We can simplify it by first distributing the slope. y-6 = -(4/5)x + 16/5. Next, add 6 to both sides. y=-(4/5)x + 46/5

Answer 2

4x +5y = 46

Explanation:

You want the line through (4, 6) perpendicular to -5x +4y = 4.

Perpendicular line

When you have the "standard form" equation of a line, ax +by = c, the perpendicular line will have the equation bx -ay = c', where the value of c' can be chosen to make the line pass through the desired point.

Starting with

-5x +4y = 4

The perpendicular line will have the form ...

4x +5y = c'

Using the given point, we can find c':

4(4) +5(6) = 16 +30 = 46 = c'

The desired equation can be written as ...

4x +5y = 46