What is an equation of the line that passes through the point (−4,3) and is perpendicular to the line 4x−3y=3

y = - x

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 )

rearrange 4x - 3y = 3 into this form

subtract 4x from both sides

- 3y = - 4x + 3 ( divide all terms by - 3 )

y = x - 1 ← in slope- intercept form

with slope m =

Given a line with slope m then the slope of a line perpendicular to it is

= - = - = -

y = - x + c ← is the partial equation

To find c substitute (- 4, 3) into the partial equation

3 = 3 + c ⇒ c = 3 - 3 = 0

y = - x ← equation of line

So firstly, we must remember that perpendicular lines have slopes that are negative reciprocals of each other. Now to find the slope of the given line, the easiest method is to convert the standard form equation into slope-intercept. Firstly, subtract both sides by 4x:

Next, divide both sides by -3:

Now the given line is in slope-intercept form. Given this slope-intercept form, we can see that the slope is 4/3. And with this information, our line's slope is going to be -3/4 (since it's the negative reciprocal).

Now, using the slope-intercept form plug the slope of our new line into the m variable and plug (-4,3) into the x and y variable to solve for b as such:

Now with all of our information, the equation for our line is . However, since the given line was in standard form (and it wasn't stated which form the line had to be in) we will put our new line in standard form.

Firstly, add both sides by 3/4x:

Next, we want to make 3/4 an integer. To do this, multiply both sides by 4:

In short:

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introduction, methodology, results, discussion

step-by-step explanation:

an observational study is one which consists of actual observation to record data and then analyse the data.

there are a number of factors that should be analyzed before starting an observational study.

the main four factors are:

i) introduction:   this should be analysed to check whether the purpose of the study is correctly established and the data recorded are appropriate for the study

methodology:   the method of collecting the data, such as whether randomly selected, and whether sample size matches with the population to be studied, whether questions asked are easy to answer by common men, etc.

results: then results such as summary of data with comments should be studied thoroughly

discussion:   the last is the discussion, this can be either by management people or persons who are all interested , etc.