Answer:
Part A) The equation in standard form is [tex]75x-y=60[/tex]
Part B) The equation in function notation is [tex]f(x)=75x+60[/tex]
Part C) The graph in the attached figure
Step-by-step explanation:
Part A)
Let
x -----> the number of days
y ----> the total rent hat Maria has to pay for renting the coat
we have
(3,285) and (6,510)
Find the slope of the linear equation
[tex]m=(510-285)/(6-3)=75\frac{\$}{day}[/tex]
Find the equation of the line into point slope form
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=75[/tex]
[tex](x1,y1)=(3,285)[/tex]
substitute
[tex]y-285=75(x-3)[/tex] ----> equation of the line into slope point form
Find the equation of the line into slope intercept form
[tex]y=mx+b[/tex]
[tex]y=75x-225+285[/tex]
[tex]y=75x+60[/tex] ----> equation of the line into slope intercept form
Find the equation of the line into standard form
[tex]Ax+By=C[/tex]
[tex]y=75x+60[/tex]
[tex]75x-y=60[/tex] -----> equation of the line into standard form
Part B) Write the equation obtained in Part A using function notation.
we have
[tex]y=75x+60[/tex]
Convert to function notation
Let
f(x)=y
substitute
[tex]f(x)=75x+60[/tex] ---> equation in function notation
Part C) Describe the steps to graph the equation obtained above on the coordinate axes
To graph the linear equation find out the intercepts
Find the y-intercept
The y-intercept is the value of y when the value of x is equal to zero
For x=0
[tex]y=75(0)+60=60[/tex]
The y-intercept is the point (0,60)
Find the x-intercept
The x-intercept is the value of x when the value of y is equal to zero
For y=0
[tex]0=75x+60[/tex]
[tex]x=-60/75=-0.8[/tex]
The x-intercept is the point (-0.8,0)
To graph the line plot the intercepts ad join the points
see the attached figure
