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ivanzaharov [21]
3 years ago
13

Write an equation of the line that pass through the given point and is (a) parallel and (b) perpendicular to the given line.

Mathematics
2 answers:
djverab [1.8K]3 years ago
6 0

Answer:

Step-by-step explanation:

Here we need to write the equations that passes through the point (4 , 3) and is parallel to the given line and perpendicular to it. So lets get started,

a)

First we calculate the slope of the given line by using any two points on the given line by the help of the formula:

m=\frac{y_2-y_1}{x_2-x_1}

we take the points (1 , 6) and (2 , 2) i chose these two you can choose any other two doesn't matter so now we calculate the slope,

m=\frac{y_2-y_1}{x_2-x_1}\\\\m=\frac{2-6}{2-1}\\\\m=\frac{-4}{1}\\\\m=-4

now since our slope is -4 and the line is parallel to the given line so the line that we need in part a would also have the same slope by the law parallel lines have same slope/gradient.

m_1=m_2

so the slope/gradient of our new line that we need which passes through the point (4,3) is -4

Now using the point slope form formula:

y-y_1=m(x-x_1)

we have our point (4,3) which corresponds to (x_1,y_1) and m which corresponds to -4 , so now

y-y_1=m(x-x_1)\\y-3=-4(x-4)\\y-3=-4x+16\\y=-4x+19

sow our new line in part a is

y=-4x+19

b)

In this part we need a line that is perpendicular to the given line which means we use the formula to calculate the slope of the perpendicular line which is:

m_1m_2=-1

where m_1=-4 the slope of our given line so the slope of the perpendicular line is,

m_1m_2=-1\\-4m_2=-1\\\\m_2=\frac{1}{4}

so using the point (4,3) and the new slope 1/4 we find the equation of the perpendicular line again by using the point-slope form formula:

y-y_1=m(x-x_1)\\y-3=\frac{1}{4}(x-4)\\\\4y-12=x-4 \\4y=x+8\\\\y=\frac{x+8}{4}\\\\y=\frac{x}{4}+2

I have attached of the graphs as well you can check it out for better understanding.

Dovator [93]3 years ago
3 0
The answer is ( 2 , 2 )
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Determine the intercepts of the line.
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Answer:

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2 years ago
|-4w+2|=14<br> the bars mean absolute value
Pie

Answer:

If you are looking for what w equals, the w would equal 3

Step-by-step explanation:

You would take the absolute value which is how far away a value is from zero.

So you would get 4w+2=14

Then you would bring the positive 2 to the other side making it negative

now we have 4w=14-2 which is the same as 4w=12

and then, you would divide 12 by 4 and then you would get 3

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5 0
3 years ago
Read 2 more answers
I need to know how to fill in the chart Ik how to plug it in it just isn't working out when I'm doing it any help?
Vanyuwa [196]
Okay so -2 would be where you plot your first point because it is B in the equation. Then you would go up 3 units (Bc it's positive) and to the right one unit (BC it's positive) The three is the same as 3/1 and it is M in the equation which is your slope so that is where I got that number from. So you just continue the pattern of up 3 over to the right 1 until you reach the end of the graph. The slope would be 3 and the y intercept will be the number that is plotted on the y axis
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The answer is no

Step-by-step explanation:

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2 years ago
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