Answer:
The equation y = [tex]-\frac{8}{7}[/tex] x - 7 represents a line perpendicular to the given line
Step-by-step explanation:
The product of the slopes of the perpendicular lines is -1, which means if the slope of one line is m, then the slope of the perpendicular line to it is [tex]\frac{-1}{m}[/tex] (negative reciprocal)
- The slope of the equation ax + by = c is [tex]\frac{-a}{b}[/tex], where a, b, c are constant
- The slope of the equation y = m x + b is m
Let us solve the question
∵ The equation of the given line is 7x - 8y = 16
∴ a = 7 and b = -8
→ Use the rule above to find the slope of it
∵ The slope of the given line = [tex]\frac{-7}{-8}[/tex]
∴ The slope of the given line = [tex]\frac{7}{8}[/tex]
To find the slope of the perpendicular line to it reciprocal the fraction and change its sign
∴ The slope of the perpendicular line = [tex]-\frac{8}{7}[/tex]
→ Look at the answer to find the equation which has this slope
∴ The equation of the perpendicular line is y = [tex]-\frac{8}{7}[/tex] x - 7
