What is an equation of the line that passes through the point (-3,-7)(−3,−7) and is parallel to the line 3x-y=53x−y=5?

y  = -3x-14

Step-by-step explanation:

Any line parallel to  

y

=

−

3

x

+

6

will be in the form  

y

=

−

3

x

+

c

for some constant  

c

If  

(

x

,

y

)

=

(

−

3

,

−

5

)

is a solution to such an equation, then replacing  

y

with  

(

−

5

)

and  

x

with  

(

−

3

)

gives

−

5

=

(

−

3

)

⋅

(

−

3

)

+

c

→

−

5

=

9

+

c

→

c

=

−

14

So the desired parallel line would have the equation

y

=

−

3

x

−

14

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.

30005

yes ok