Question

The line y=ax + b is perpendicular to the line y-3x=4 and passes through the point (1.-2). The value of 'a' an of 'b' are ?? Solution

Answer 1

`y_2=-1/3x_2-5/3`

A lot of detail given so you can see where everything comes from
With practice and application of shortcuts you should be able to solve this type of problem in just a few lines/

Explanation:

Given: `y-3x=4`

Add `3x` to both sides

`y=3x+4`

Set as `y_1=3x_1+4 " "........................Equation(1)`

The gradient for this equation is 3. So the gradient if a line perpendicular will be: `(-1)xx1/3 = -1/3`

Thus we have:

`y_2=ax_2+bcolor(white)("ddd") ->color(white)("ddd") y_2=-1/3x_2+b" "..Equation(2)`

We know that the line for `Eqn(2)` passes through the point
`(x_2,y_2)=(1,-2)` So if we substitute these values into `Eqn(2)` we are able to determine the value of `b`

`y_2=-1/3x_2+bcolor(white)("dd") ->color(white)("ddd") -2=-1/3(1)+b`

Add `1/3` to both sides

`color(white)("dddddddddddddddd")->color(white)("ddd")-2+1/3=b`

`b=-5/3` giving

`y_2=ax_2+bcolor(white)("ddd") ->color(white)("ddd") y_2=-1/3x_2-5/3`