what is the y-intercept of the equation of the line that is perpendicular to the line y=3/5x+10 and passes through the point (15
,-5)
1 answer:
The slope of the given line is the coefficient of x, 3/5. The slope of the perpendicular line will be the negative reciprocal of that: -1/(3/5) = -5/3.
The point-slope form of the equation for a line of slope m through point (h, k) can be written ...
... y = m(x -h) +k
For your point and the slope found above, this becomes
... y = (-5/3)(x -15) -5
When x=0, this is
... y = (-5/3)(-15) -5 = 20
The y-intercept is 20.
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Answer:
The interval for which <em>y</em> is a decreasing function of <em>x</em> is:
Or as an inequality:
Step-by-step explanation:
We are given the equation:
And we want to find the range of values <em>x</em> for which <em>y</em> is a decreasing function of <em>x</em>.
<em>y</em> is decreasing whenever <em>y'</em> is negative. Find <em>y'</em> using the Quotient Rule:
Differentiate:
<em>y</em> is decreasing whenever <em>y'</em> is negative. Thus:
Multiply both sides by <em>x²</em>. This is always positive so we do not need to change the sign:
Factor:
e<em>ˣ</em> is always positive. So:
Adding one to both sides produces:
Therefore, <em>y</em> is a decreasing function of <em>x</em> when <em>x</em> is less than one (and greater than 0).
In interval notation:
Or as an inequality:
Answer:
4b = 8
Step-by-step explanation:
Given 12b = 24
This is written as (4 X 3)b = 24
⇒ 4b X 3 = 24
Dividing by 3 throughout, we have
4b = = 8.
Therefore, the value of 4b is 8.