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Anettt [7]
3 years ago
5

The line passes through (9,8) and is perpendicular to x-2y=-16

Mathematics
1 answer:
pickupchik [31]3 years ago
4 0

The equation of line perpendicular to x-2y=-16 passing through (9,8) is: y=-2x+26

Step-by-step explanation:

Given

x-2y=-16\\Adding\ 2y\ on\ both\ sides\\x=2y-16\\Adding\ 16\ on\ both\ sides\\x+16=2y-16+16\\x+16=2y\\2y=x+16\\Dividing\ both\ sides\ by\ 2\\\frac{2y}{2}=\frac{x+16}{2}\\y=\frac{x}{2}+\frac{16}{2}\\y=\frac{1}{2}x+8\\

The equation is in slope-intercept form,  the coefficient of x will be the slope of given line. The slope is: 1/2

As the product of slopes of two perpendicular lines is -1.

\frac{1}{2}*m=-1\\m=-1*\frac{2}{1}\\m=-2

Slope intercept form is:

y=mx+b

Putting the value of slope

y=-2x+b

To find the value of b, putting (9,8) in the equation

8=-2(9)+b\\8=-18+b\\b=8+18\\b=26

Putting the values of b and m

y=-2x+26

Hence,

The equation of line perpendicular to x-2y=-16 passing through (9,8) is: y=-2x+26

Keywords: Equation of line, Slope-intercept form

Learn more about equation of line at:

  • brainly.com/question/1993757
  • brainly.com/question/2048256

#LearnwithBrainly

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67. The line contains the point (4,0) and is parallel<br> to the line defined by 3x = 2y.
olganol [36]

Answer:

y=\frac{3}{2} x-6

Step-by-step explanation:

Hi there!

<u>What we need to know:</u>

  • Linear equations are typically organized in slope-intercept form:
  • y=mx+b where m is the slope of the line and b is the y-intercept (the value of y when the line crosses the y-axis)
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<u>1) Determine the slope of the parallel line</u>

Organize 3x = 2y into slope-intercept form. Why? So we can easily identify the slope, m.

3x = 2y

Switch the sides

2y=3x

Divide both sides by 2 to isolate y

\frac{2y}{2} = \frac{3}{2} x\\y=\frac{3}{2} x

Now that this equation is in slope-intercept form, we can easily identify that \frac{3}{2} is in the place of m. Therefore, because parallel lines have the same slope, the parallel line we're solving for now will also have the slope \frac{3}{2} . Plug this into y=mx+b:

y=\frac{3}{2} x+b

<u>2) Determine the y-intercept</u>

y=\frac{3}{2} x+b

Plug in the given point, (4,0)

0=\frac{3}{2} (4)+b\\0=6+b

Subtract both sides by 6

0-6=6+b-6\\-6=b

Therefore, -6 is the y-intercept of the line. Plug this into y=\frac{3}{2} x+b as b:

y=\frac{3}{2} x-6

I hope this helps!

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