Answer :
Answer:
The slope of a line perpendicular to this line is 9/8
The slope of a line parallel to this line is -8/9
Explanation:
Given:
8x + 9y = 2
To find:
a) The slope of the line perpendicular to the given line
b) The slope of the line parallel to the given line
a) To determine the line perpendicular to 8x + 9y = 2, we need to first find its slope
[tex]\begin{gathered} \text{8x + 9y = 2} \\ 9y\text{ = 2 - 8x} \\ y\text{ = }\frac{2-8x}{9} \\ y\text{ = }\frac{2}{9}\text{ - }\frac{8}{9}x \\ \\ In\text{ equation of line: y = mx + b} \\ m\text{ = slope, b = y-intercept} \\ \\ slope\text{ = -8/9} \end{gathered}[/tex]For two lines to be perpendicular, the slope of one line will be the negative reciprocal of the second line
slope of the 1st line = -8/9
reciprocal of the line = -(9/8) = -9/8
negative reciprocal = -(-9/8) = 9/8
This means the second line will have a slope of 9/8
The slope of a line perpendicular to this line is 9/8
b) For two lines to be parallel, the slope of both lines will be the same.
Since slope of the first is -8/9. The slope of the second line will also be -8/9
The slope of a line parallel to this line is -8/9