Answer:
Part A) [tex]y=4,000m+5,000[/tex]
Part B) see the explanation
Part C) The graph in the attached figure )see the explanation)
Step-by-step explanation:
Part A)
Let
x ----> the number of months worked
y ----> Brian's wages in dollars
we know that
The linear equation in slope intercept form is equal to
[tex]y=mx+b[/tex]
where
m is the slope or unit rate of the linear equation
b is the y-intercept or initial value
In this problem we have
The slope is equal to [tex]m=\$4,000\ per\ month[/tex]
The y-intercept is [tex]b=\$5,000[/tex]
substitute
[tex]y=4,000x+5,000[/tex]
For x=m months
substitute
[tex]y=4,000m+5,000[/tex]
Part B) Complete the table
we have the expression
[tex]y=4,000x+5,000[/tex]
Substitute each value of x in the expression above to obtain the value of y
For x=1 -----> [tex]y=4,000(1)+5,000=\$9,000[/tex]
For x=2 -----> [tex]y=4,000(2)+5,000=\$13,000[/tex]
For x=4 -----> [tex]y=4,000(4)+5,000=\$21,000[/tex]
For x=7 -----> [tex]y=4,000(7)+5,000=\$33,000[/tex]
Find the ratio of y:x
For x=1, y=9,000 -----> [tex]y:x=9,000:1[/tex]
For x=2, y=13,000 -----> [tex]y:x=13,000:2=6,500:1[/tex]
For x=4, y=21,000 -----> [tex]y:x=21,000:4=5,250:1[/tex]
For x=7, y=33,000 -----> [tex]y=33,000:7=4,714.29:1[/tex]
The ratio of y:x are not equal, that means that the situation is not proportional
Part C) Graph the points from the table and connect them
using a graphing tool
The graph in the attached figure
Remember that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]k=\frac{y}{x}[/tex] or [tex]y=kx[/tex]
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 graph, the line not passes though the origin, that means that the graph is not proportional
