All categories

3 years ago

How to write an equation of the line through the point (-2,1) that is perpendicular to the line 5x+9y=-9

Mathematics

1 answer:

Julli [10]3 years ago

6 0

Answer:

$\large\boxed{y=\dfrac{5}{9}x+\dfrac{19}{9}}$

Step-by-step explanation:

$\text{Let}\\\\k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\l\ \parallel\ k\iff m_1=m_2\\\\===================================\\\\\text{We have the equation i the standard form.}\\\text{ Convert it to the slope-intercept form}\ y=mx+b:\\\\5x+9y=-9\qquad\text{subtract}\ 5x\ \text{from both sides}\\\\9y=-5x-9\qquad\text{divide both sides by 9}\\\\y=-\dfrac{5}{9}x-1\to m_1=-\dfrac{5}{9}\\\\m_2=-\dfrac{1}{m_1}\to m_2=-\dfrac{1}{-\frac{5}{9}}=\dfrac{9}{5}$

$\text{We have the equation:}\\\\y=\dfrac{5}{9}x+b\\\\\text{Put the coordinates of the point (-2, 1) to the equation:}\\\\1=\dfrac{5}{9}(-2)+b\\\\1=-\dfrac{10}{9}+b\qquad\text{add}\ \dfrac{10}{5}\ \text{to both sides}\\\\\dfrac{19}{9}=b\to b=\dfrac{19}{9}$

You might be interested in

What is 3 × 8000283743729.

Keith_Richards [23]

Dear user,

3 × 8000283743729 = 2.4000851

7 0

3 years ago

Read 2 more answers

Under a dilation, the point (3, 5) is moved to (6, 10).

Vsevolod [243]

The scale factor of the dilation is 2

4 0

3 years ago

Read 2 more answers

I need help on this question

xeze [42]

Circle graph is the best answer and the right one.

8 0

3 years ago

If I have a <img src="https://tex.z-dn.net/?f=4%20%5Ctimes%204" id="TexFormula1" title="4 \times 4" alt="4 \times 4" align="absm

SOVA2 [1]

Answer:

576 ways

Step-by-step explanation:

There are 4 choices for the column of pawn in the 1st row

There are 3 choices for the column of pawn in the 2nd row,

There are 2 choices for the column of pawn in the 3rd row, and

There is 1 choice for the column of the pawn in the 4th row

Which gives a total of 4! = 24

Also, the pawns are distinct, so there are 4! ways to place them in these chosen positions;

4! = 24

So, there are 24 * 24 possible ways

= 576 ways

7 0

3 years ago

Write the equation in slope-intercept form of the line that includes the point (3,2) and has a slope of 4/3.

UkoKoshka [18]

Answer:

$y = \frac{4}{3}x - 2$

Step-by-step explanation:

Given:

Slope (m) = ⁴/3

Point on the line = (x, y) = (3, 2)

Required:

Write the equation in slope-intercept form which is y = mx + b

Solution:

Since we know the slope(m), we need to find the y-intercept (b).

This, substitute (x, y) = (3, 2) and m = ⁴/3 into y = mx + b, and solve for b. Thus:

2 = ⁴/3(3) + b

2 = 4 + b

2 - 4 = b

-2 = b

b = -2

To write the equation, substitute m = ⁴/3 and b = -2 into y = mx + b

$y = \frac{4}{3}x - 2$

4 0

2 years ago