Question

Write An equation Perpendicular to the given equation through the ordered pair y=4x+6(1,-3).
Please Show Steps,Instruction on how to solve this ..Thanxx

Answer 1

perpendicular to the given like has a gradient of -1/4 as the product of the gradients is -1

then using point gradient formula

y + 3 = -1/4(x - 1)

4y + 3 = -x + 1

or x + 4y + 2 = 0

or y = -1/4 x -2

Answer 2

The general formula of a straight line is: y = mx + c
Where m is the gradient and c is the y-intercept.

So the gradient of the line you have been given is 4. This means the gradient of a line perpendicular to it will have a gradient of "-1/4"
You can find this by = this equation
gradient of eq1 * gradient of line perpendicular = -1
so
\[4 \times x = -1\]
\[x= -1/4 \]
So the line will have the equation:
y = -1/4x + c where c is the y-intercept

then u have to use the gradient formular (y-y1) = m(x-x1)
\[y-(-3)=\frac{1}{4}(x-(1))\]
\[y+3=-\frac{1}{4}x +\frac{1}{4}\]
y= -1/4x-11/4