Ask question

Ask question

All categories

3 years ago

15

Find an equation of the line passing through each of the following pairs of points. a (−3, 1), (0, 3)

1 answer:

Svetlanka [38]3 years ago

5 0

$\bf (\stackrel{x_1}{-3}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{3}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{3}-\stackrel{y1}{1}}}{\underset{run} {\underset{x_2}{0}-\underset{x_1}{(-3)}}}\implies \cfrac{2}{0+3}\implies \cfrac{2}{3}$

$\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{1}=\stackrel{m}{\cfrac{2}{3}}[x-\stackrel{x_1}{(-3)}]\implies y-1=\cfrac{2}{3}(x+3) \\\\\\ y-1=\cfrac{2}{3}x+2\implies y=\cfrac{2}{3}x+3$

You might be interested in

a buisnees has a 20p ft wall and places 6 ft letters on the center of the exterior wall to spell sale. If there is 1ft between e

Nezavi [6.7K]

200-6 = 194

<h2>194 / 2 = 97 </h2>

4 0

3 years ago

Which choice is equivalent to the fraction below when x is an appropriate value? Hint: Rationalize the denominator and simplify.

densk [106]

$\frac{3}{3- \sqrt{6x} } = \frac{3}{3- \sqrt{6x} } \times \frac{3+ \sqrt{6x} }{3+ \sqrt{6x} } \\ = \frac{3(3+ \sqrt{6x})}{3^2-( \sqrt{6x} )^2} = \frac{3(3+ \sqrt{6x})}{9-6x} \\ =\frac{3(3+ \sqrt{6x})}{3(3-2x)}=\frac{3+ \sqrt{6x}}{3-2x}$

6 0

3 years ago

Read 2 more answers

Match the reasons with the statements in the proof.

Len [333]

Observe the given figure.

Given: $m \angle 1 = m \angle 3, m \angle 2 = m \angle 3$

To prove: $l \parallel m$

Statement

1. $m \angle 1 = m \angle 3, m \angle 2 = m \angle 3$

Reason: Given

2. $m \angle 1 = m \angle 2$

Reason: Substitution

3. $\angle 1,\angle 2$ are alternate interior angles.

Reason: Definition of alternate interior angles

4. $l \parallel m$

Reason: If alternate interior angles are equal, then the lines are parallel.

7 0

4 years ago

Read 2 more answers

Does the data in the table represent a direct variation or an inverse variation? Write an equation to model the data in the tabl

MakcuM [25]

The equation for the direct variation is y= kx (where k is contant of variation.)

This equation represent that if x will increase then y will also increase because it's k times x.

Where the equation for indirect variation is $y=\frac{1}{k} x$

By this equation if x will increase then y will decrease and vice versa.

The given data is :

x: 2 4 8 12

y: 4 2 1 2/3

Notice as x is increasing then y is decreasing. Like x has increased from 2 to 4 then y is decresing from 4 to 2 and so on.

So, the given data represent an indirect variation.

7 0

3 years ago

I WILL MARK BRAINIEST

serg [7]

Answer:

h = 40.5 m

A) 1 : 9

B) 1 : 3

C) 40.5 m

Step-by-step explanation:

Let the height of the larger triangle be h

Therefore,

$\frac{10}{90}= \frac{4.5}{h}\\\\\frac{1}{9}= \frac{4.5}{h}\\\\h = 9\times 4.5\\\\h = 40.5\:m\\$

A)

The ratio of the area of small triangle to the large triangle

$=\frac{10}{90}=\frac{1}{9}=1 : 9$

B)

The ratio of the side length of small triangle to the side length of large triangle

$=\sqrt{\frac{10}{90}} =\sqrt {\frac{1}{9}} =1 : 3$

C) The height of the larger triangle is <u>40.5 m</u>

5 0

3 years ago