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3 years ago

Line j goes through the point (-7, 5) and is perpendicular to 2x – 3y = -18. Find the equation of line j.

Mathematics

1 answer:

Alex777 [14]3 years ago

5 0

Answer:

3x + 2y = 31

Step-by-step explanation:

Solve the given equation for y to determine the slope of this line:

-3y = -2x = -18, so that y = (2/3)x + 6.

Therefore, a line perpendicular to the given line has the slope -3/2, which is the negative reciprocal of this 2/3.

Using the slope-intercept formula y = mx + b and inserting the knowns (slope = m = -3/2, y = 5 and x = -7), we obtain:

5 = (3/2)(-7) + b, or (after multiplying all terms by 2):

10 = -21 + 2b, or 2b = 31, or b = 31/2.

Then the equation is y = (-3/2)x + 31/2.

Let's put this into standard form. Multiply all terms by 2, obtaining:

2y = -3x + 31, or

3x + 2y = 31 This is the equation of the perpendicular line in question.

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Answer:

Kim will need to spend 67 minutes on her sixth ride

Step-by-step explanation:

Represent the number of minutes of her sixth ride by m.

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3 years ago

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Read 2 more answers

Consider the graph of the line y = .5x- 4 and the point

Katena32 [7]

Answer:

slope of parallel line and perpendicular line are 5 and -1/5 espectively

equation of parallel and perpendicular line are y = 5x + 22 $y= \frac{-1}{5} x+\frac{6}{5}$ respectively

Step-by-step explanation:

y = 5x - 4 is in the form

y = mx + c

where m is the slope of the line and c is the y intercept of thr line

therefore slope of the line = 5 and y intercept = -4

when an another line is parallel to the given line then the slope of both the lines are equal

therefore the slope the parallel line = 5

equation of a line passing through a given point $(x_{1} ,y_{1})$ with slope m is given by $y-y_{1} = m(x-x_{1} )$

given $(x_{1} ,y_{1})$ = (-4,2)

therefore equation of line y-2 = 5(x+4)

therefore y = 2+ 5x+20

y = 5x + 22is the eqaution of required line.

when two lines are perpendiculer then

$m_{1} m_{2}=-1$

where $m_{1} and m_{2}$ are slope of the lines therefore

m×5=-1

therefore m= $\frac{-1}{5}$

therefore eqaution of line passing through (-4,2) and with slope m= $\frac{-1}{5}$ is given by $y - 2= \frac{-1}{5} (x+4)$

$y= \frac{-1}{5} x+\frac{6}{5}$

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3 years ago