Question

Find the equation of the line that contains the point (-2, -1) and is perpendicular

to the line 2x + 3y = 9. Write the line in slope-intercept form, if possible. Graph the
lines
Select the correct choice below and fill in the answer box to complete your
choice.
O A. The equation of the perpendicular line in slope-intercept form is
(Simplify your answer. Type your answer in slope-intercept form. Use
integers or fractions for any numbers in the equation.)
B. The equation of the perpenditular line cannot be written in
slope-intercept form. The equation of the perpendicular line is
(Simplify your answer. Use integers or fractions for any numbers in the
equation.)

Answer 1

The line equation in the slope-intercept form:

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

Explanation:

We know that the slope-intercept of line equation is

`y = mx+b`

Where m is the slope and b is the y-intercept

Given the line

`2x + 3y = 9`

Writing in the slope-intercept form

`2x + 3y = 9`

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

Therefore, the slope of the line = 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 slope = – 1/m

`=-(1)/(-(2)/(3))=(3)/(2)`

Given the point

(x₁, y₁) = (-2, -1)

Using the point-slope form of the line equation

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

where m is the slope and (x₁, y₁) is the point

substituting the perpendicular slope m = 3/2 and the point (-2, -1)

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

Writing in the slope-intercept form

`y+1=(3)/(2)\left(x+2\right)`

subtract 1 from both sides

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

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

Thus, the line equation in the slope-intercept form:

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