What is the slope-intercept form of the line that is perpendicular to 3x - 2y = 8 and passes through the point (-1, -1)?

What is the slope-intercept form of the line that is perpendicular to 3x - 2y = 8 and passes through the point (-1, -1)?

• A. y = -(2/3)x - 5/3
• B. y = (3/2)x + 1
• C. y = (2/3)x - 5
• D. y = -(3/2)x - 1

Answer: (A)

To determine the correct slope-intercept form of the line that is perpendicular to the given equation \(3x - 2y = 8\) and passes through the point \((-1, -1)\), we first need to find the slope of the line described by the equation. 1. **Convert to slope-intercept form (y = mx + b)**: Start with the equation \(3x - 2y = 8\). Rearranging it, we can isolate \(y\): \[ -2y = -3x + 8 \] \[ y = \frac{3}{2}x - 4 \] From this form, we see that the slope (m) of the line is \(\frac{3}{2}\). 2. **Find the slope of the perpendicular line**: The slope of a line that is perpendicular to another is the negative reciprocal of the original slope. Consequently, the negative reciprocal of \(\frac{3}{2}\) is \(-\frac{2}{3}\). 3. **Use the point-slope form to find the equation of the new line**: We have the slope \(-

To determine the correct slope-intercept form of the line that is perpendicular to the given equation (3x - 2y = 8) and passes through the point ((-1, -1)), we first need to find the slope of the line described by the equation.

1. Convert to slope-intercept form (y = mx + b): Start with the equation (3x - 2y = 8). Rearranging it, we can isolate (y):

[

-2y = -3x + 8

]

[

y = \frac{3}{2}x - 4

]

From this form, we see that the slope (m) of the line is (\frac{3}{2}).

2. Find the slope of the perpendicular line: The slope of a line that is perpendicular to another is the negative reciprocal of the original slope. Consequently, the negative reciprocal of (\frac{3}{2}) is (-\frac{2}{3}).

3. Use the point-slope form to find the equation of the new line: We have the slope (-