What is the equation, in point-slope form, of the line that is parallel to the given line and passes through the point (4, 1)?
y − 1 = −2(x − 4)
y – 1 = Negative one-half(x – 4)
y – 1 = One-half(x – 4)
y − 1 = 2(x − 4)

We know that two lines are parallel if they have the same slope.

Using this, we will find that the line parallel to the one graphed and that passes through (4, 1) is: y = -2*x + 9

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Let's see how we can find the line:

To find the line, the first thing we need to do is find the slope of the graphed line.

Remember that a general line is something like:

y = a*x + b

Where a is the slope and b is the y-intercept.

If we do know that the line passes through the points (x₁, y₁) and (x₂, y₂) then the slope of that line can be written as:

Here we can see that the graphed line passes through (-3, 3) and (-2, 1). Then the slope will be:

Then the slope of the parallel line is also -2, so the parallel line will be something like:

y = -2*x + c

To find the value of c, we use the fact that this line passes through (4, 1).

So when x = 4, we must have y = 1.

Repacing these in the line equation we get:

1 = -2*4 + c

1 = -8 + c

1 + 8 = c = 9

Then the parallel line to the graphed one that passes through (4, 1) is:

y = -2*x + 9

If you want to learn more, you can read:

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Given:

The line parallel to the given line containing the points (-3,3) and (-2,1).

Also, the parallel line passes through the point (4,1).

We need to determine the equation of the line in slope - intercept form.

Slope:

Since, the two lines are parallel, then their slopes are equal.

Thus, the slope of the parallel line can be determined using the formula,

Substituting the points (-3,3) and (-2,1), we get;

Thus, the slope of the line is

Equation of the line:

The equation of the line can be determined using the formula,

Since, the line passes through the point (4,1), let us substitute the point (4,1) in the above formula, we have;

Thus, the equation of the line is

Hence, Option a is the correct answer.

step-by-step explanation:

30% of $420 is 0.30($420) = $126 and $420 + $126 = $546.

or, 130% of $420 is 1.3($420) = $546.

notice that this is not the $600 original list price with which we started.

why doesn't this work?

the method does not work because 30% of $420 is not the same amount as the 30% of $600. it may seem obvious when stated this way, but it is a very common error made on problems of this type. we cannot just use the same percent and get back to the original amount because we are taking that percent of a different value.

to work problems of this type correctly, it is generally best to write an equation for the situation and then solve.

example: since (100% – 30%)(original price) = (sale price)

70% of the   (original price) is $420.

0.7x   = 420

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x = 600

the original cost was $600.

we may also solve this problem using the two-step method. working the problem in two steps requires us to use more algebra skills. we have to know that x = 1x (identity property of multiplicationtext annotation indicator) and that 1x – 0.3x = 0.7x (subtracting like terms). then we solve the problem as follows:

(original price) – 30%(original price) = sale price

x – 0.3x = 420

0.7x = $420

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x = 600

the original cost was $600.  

note that with both of the above methods we do obtain the correct original amount.

example: after a 5% pay raise, hermione is earning $22,680 per year. what was she earning before the pay raise?

105% of (original salary) = current salary

1.05x = 22,680

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x = 21,600

hermione earned $21,600 per year before the pay raise.

this is an example so maybe you will get how to at least do it!

yes because they have the same amount of green and blur marbles.

step-by-step explanation: