Question

Consider the line 8x+9y=2What is the slope of a line perpendicular to this line? What is the slope of a line parallel to this line? Slope of a perpendicular line: Slope of a parallel line:

Answer 1

The slope of a line perpendicular to the line 8x + 9y = 2 is 9/8. The slope of a line parallel to the line 8x + 9y = 2 is -8/9.

Step-by-step explanation:

The equation of the given line is 8x + 9y = 2. To find the slope of a line perpendicular to this line, we need to find the negative reciprocal of the slope of this line. The slope-intercept form of a line is y = mx + b, where m represents the slope. We can rearrange the given equation in this form: y = (-8/9)x + (2/9). Comparing this equation with the slope-intercept form, we can see that the slope of the line is -8/9. The negative reciprocal of -8/9 is 9/8. Therefore, the slope of a line perpendicular to the given line is 9/8.

To find the slope of a line parallel to the given line, we use the fact that parallel lines have the same slope. So, the slope of a line parallel to the given line is also -8/9.

Answer 2

we have the equation

8x+9y=2

isolate the variable y

9y=-8x+2

y=-(8/9)x+2/9 -----> Equation in slope-intercept form

The slope of the given line is m=-8/9

so

Part 1

If two lines are perpendicular, then their slopes are negative reciprocal

that means

The slope of the perpendicular line is m=9/8

Part 2

If two lines are parallel, then their slopes are equal

therefore

The slope of the parallel line is m=-8/9