what is the equation of a line that is parallel to 2x+3y=3 and passes through the point (3,−4)?

Paralell has same slope
the slope for ax+by=c is -a/b
that means that a line paralell to 2x+3y=3 will have 2x+3y=something
find that something

given
(3,-4)
x=3 and y=-4 is a soltuion
2x+3y=something
2(3)+3(-4)=something
6-12=something
-6=something

2x+3y=-6

What am i doing here. add?

Answer

1 number

explanation

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.