Question

Through (-4,3) , perpendicular to m=-2/3​

Answer 1

The equation of the line:

`y=(3)/(2)x+9`

Explanation:

Given

• The point (-4, 3)

• m = -2/3

We know that a line perpendicular to another line contains a slope that is the negative reciprocal of the slope of the other line, such as:

slope = m = -2/3

perpendicular to m = -1/m

`=-(1)/(\left((-2)/(3)\right))=(3)/(2)`

Using the point-slope form of the line equation

`y-y_1=m\left(x-x_1\right)`

substituting the values m = 3/2 and the point (-4, 3)

`y-3=(3)/(2)\left(x-\left(-4\right)\right)`

`y-3=(3)/(2)\left(x+4\right)`

Add 3 to both sides

`y-3+3=(3)/(2)\left(x+4\right)+3`

`y=(3)/(2)x+9`

Thus, the equation of the line:

`y=(3)/(2)x+9`