Determine whether the point 1,5 is a solution to the system of inequalities below y>3x , y>/2x+1
What is the best first step to write this linear equation in slope-intercept form?
1 answer:
Answer:
subtract the term in "x" (1/7 x) on both sides of the equal sign
Step-by-step explanation:
Recall that in order to get a linear equation in slope-intercept form, all is needed is to solve for for "y" in the equation. That means isolate the variable "y" on one side of the equal sign.
In order to do such, all is needed in the given equation: , is to subtract the term in "x" on both sides of the equal sign, so the term disappears on the left, leaving the variable "y" on its own:
This last expression is now the equation of the line in slope-intercept form.
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Derivative of the denominator:
Hmm our numerator is 2x+7. Ok this let's us know that a simple u-substitution is NOT going to work. But let's apply some clever Algebra to the numerator splitting it up into two separate fractions. Split the +7 into +2 and +5.
and then split the fraction,
Based on our previous test, we know that a simple substitution will work for the first integral:
So the first integral changes,
integrating to a log,
Other one is a little tricky. We'll need to complete the square on the denominator. After that it will look very similar to our arctangent integral so perhaps we can just match it up to the identity.
So we have this going on,
Let's factor the 5 out of the intergral,
and the 4 from the denominator,
Bringing all that stuff together as a single square,
Making the substitution:
giving us,
simplying a lil bit,
and hopefully from this point you recognize your arctangent integral,
undo your substitution as a final step,
and include a constant of integration,
Hope that helps!
Lemme know if any steps were too confusing.