Answer:
Step-by-step explanation:
A linear function has been given as,
y = [tex]\frac{1}{3}x+5[/tex]
Comparing it with the slope intercept equation,
y = mx + b
b = y-intercept = 5
From the graph,
y-intercept = (-2)
From the given table,
For x = 0, f(x) = 3
Therefore, y-intercept = 3
A line passes through two points (-3, -2) and (3, 0),
Slope of the line = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
= [tex]\frac{0+2}{3+3}[/tex]
= [tex]\frac{1}{3}[/tex]
Equation of a line passing through a point (x', y') and slope = m
y - y' = m(x - x')
If the point is (3, 0) and slope = [tex]\frac{1}{3}[/tex]
y - 0 = [tex]\frac{1}{3}(x-3)[/tex]
y = [tex]\frac{1}{3}x-1[/tex]
y-intercept of this line = (-1)
Therefore, decreasing order of the slopes will be,
[tex]5>3>\frac{1}{3}>(-2)[/tex]
Order of the functions with slopes from maximum to lease will be,
1). [tex]y=\frac{1}{3}x+5[/tex]
2). Function represented by the table.
3). Line passing through (-3, -2) and (3, 0)
4). Function shown in the graph
