Answer:
Part 2) Option D. yes; k = 1/4 and y = 1/4x
Part 6) Option D. y = 1/5x-1
Part 8) Option C. line b
Part 11) Option D. -1/5
Part 15) Option A. line a
Step-by-step explanation:
Part 2) we know that
A relationship between two variables, x, and y, represent a directly variation if it can be expressed in the form
In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin
In this problem the line passes through the origin
therefore
Yes. y varies directly with x
Let
A(4,1)
The constant k is equal to
substitute
the equation is equal to
Part 6) we know that
The y-intercept of the trend line is -1 (For x=0)
The slope of the trend line is positive
The x-intercept of the trend line is 5 (For y=0)
therefore
the equation is equal to
Part 8) we have
This is the equation of a line into point slope form
The slope is negative
Pass through the point (0,-4) ----> y-intercept
The x-intercept is equal to
therefore
Is the line b
Part 11)
What is the slope of the line through the points (–2, –1) and (8, –3)?
we know that
The formula to calculate the slope between two points is equal to
substitute the values
simplify
Part 15) we have
The slope is positive
The y-intercept is -2 (For x=0)
The x-intercept is (For y=0)
therefore the line is a