Answer:
The missing number in the green box is 4
Step-by-step explanation:
The product of the slopes of the perpendicular lines is -1, which means
- if the slope of one of them is m, then the slope of the perpendicular line to it is the negative reciprocal ([tex]\frac{-1}{m}[/tex])
The slope-intercept form of the linear equation is y = m x + b, where
- m is the slope of the line
Let us solve the question
∵ The equation of the first line is y = 4x + 2
→ Compare it with the form of the linear equation above
∴ m = 4
∵ m is the slope
∴ The slope of the line is 4
∵ The slope of the perpendicular line should be the negative reciprocal of it
∵ The negative reciprocal of 4 is [tex]-\frac{1}{4}[/tex]
∴ The slope of the perpendicular line is [tex]-\frac{1}{4}[/tex]
→ Substitute it in the equation
∴ y = [tex]-\frac{1}{4}[/tex] x + 2
∴ The missing number in the green box is 4
