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2 years ago

Write the equation of a line perpendicular to 5x – 4y = - 3 that passes through the point (-5,2).

Mathematics

1 answer:

kolezko [41]2 years ago

4 0

Answer: 5y + 4x = - 10

Step-by-step explanation:

Two lines are said to be perpendicular if the product of their gradients = -1.

If the gradient of the first line is $m_{1}$ and the gradient of the second line is $m_{2}$ , if the lines are perpendicular, them

$m_{1}$ x $m_{2}$ = -1 , that is

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

The equation of the line given is 5x - 4y = -3 , we need to write this equation in slope - intercept form in order to find the slope.

The equation in slope -intercept form is given as :

y =mx + c , where m is the slope and c is the y - intercept.

Writing the equation in this form , we have

5x - 4y = + 3

4y = 5x -+3

y = 5x/4 + 3/4

comparing with the equation y = mx + c , then $m_{1}$ = 5/4

Which means that $m_{2}$ = -4/5 and the line passes through the point ( -5 , 2 ).

Using the equation of line in slope - point form to find the equation of the line;

y - $y_{1}$ = m ( x - $y_{1}$ )

y - 2 = -4/5 ( x +5)

5(y - 2 ) = -4 ( x + 5 )

5y - 10 = -4x - 20

5y + 4x = - 10

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Write an equation in slope-intercept form for the line that passes through the point ( -1 , -2 ) and is perpendicular to the l

mamaluj [8]

The equation in slope-intercept form for the line that passes through the point ( -1 , -2 ) and is perpendicular to the line − 4 x − 3 y = − 5 is $y = \frac{3}{4}x - \frac{5}{4}$

Solution:

The slope intercept form is given as:

y = mx + c ----- eqn 1

Where "m" is the slope of line and "c" is the y - intercept

Given that the line that passes through the point ( -1 , -2 ) and is perpendicular to the line − 4 x − 3 y = − 5

Given line is perpendicular to − 4 x − 3 y = − 5

− 4 x − 3 y = − 5

-3y = 4x - 5

3y = -4x + 5

$y = \frac{-4x}{3} + \frac{5}{3}$

On comparing the above equation with eqn 1, we get,

$m = \frac{-4}{3}$

We know that product of slope of a line and slope of line perpendicular to it is -1

$\frac{-4}{3} \times \text{ slope of line perpendicular to it}= -1\\\\\text{ slope of line perpendicular to it} = \frac{3}{4}$

Given point is (-1, -2)

Now we have to find the equation of line passing through (-1, -2) with slope $m = \frac{3}{4}$

Substitute (x, y) = (-1, -2) and m = 3/4 in eqn 1

$-2 = \frac{3}{4}(-1) + c\\\\-2 = \frac{-3}{4} + c\\\\c = - 2 + \frac{3}{4}\\\\c = \frac{-5}{4}$

$\text{ substitute } c = \frac{-5}{4} \text{ and } m = \frac{3}{4} \text{ in eqn 1}$

$y = \frac{3}{4} \times x + \frac{-5}{4}\\\\y = \frac{3}{4}x - \frac{5}{4}$

Thus the required equation of line is found

8 0

2 years ago

A bag contains 9 red marbles, 18 orange marbles, 2 yellow marbles, and 5 purple marbles. A marble is drawn at random from the ba

vlada-n [284]

Answer:

8/17

Step-by-step explanation:

total balls= 9 + 18 + 2 + 5 = 34

balls drawn should NOT be Orange.

so, 34 - 18 (as there are 18 orange balls)

16 balls

probability= 16/34 = 8/17

answer = 8/17

7 0

3 years ago

The table below represents a linear function f(x) and the equation represents a function g(x):

Aneli [31]

Slope of f(x)

Slope of g(x)

PART A)
The slopes of f(x) and g(x) are the same.

PART B)
The equation for line f(x)
y = 4x + b
-1 = 4(0) + b
-1 = b

y = 4x - 1

The function G(x) has a bigger y-intercept. The y-intercept of g(x) is 3, while the y-intercept of f(x) is -1.

4 0

3 years ago

Write 6.7 in two other forms

salantis [7]

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