“ write the equation of the line that goes through the point (6,3) and is parallel to y=-2/3x+5 “ ????

Mathematics

1 answer:

brilliants [131]3 years ago

5 0

Answer:

see explanation

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - $\frac{2}{3}$ x + 5 ← is in slope- intercept form

with slope m = - $\frac{2}{3}$

Parallel lines have equal slopes, thus

y = - $\frac{2}{3}$ x + c ← is the partial equation of the line

To find c substitute (6, 3) into the partial equation

3 = - 4 + c ⇒ c = 3 + 4 = 7

y = - $\frac{2}{3}$ x + 7 ← equation of line

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<em>Comment on the question</em>

The directive to "compare the volumes" does not tell anything about the sort of comparison you are expecting. We note that the expression x^3-x^2 is zero or less up to the point where x=1, so we wonder exactly what it is supposed to be modeling. Any real volume will not be negative.

For small values of x, the quadratic is quite a bit larger. However, we know the cubic will grow larger than any quadratic for large values of x. So, the comparison you get will depend on the domain of interest—which is not specified.