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Sergeeva-Olga [200]

4 years ago

11

2x + 3y = 1,470 Change the equation to slope-intercept form. Identify the slope and y-intercept of the equation. Be sure to show

all your work.

2 answers:

Ilya [14]4 years ago

7 0

2x + 3y = 1470 ...subtract 2x from both sides
3y = -2x + 1470 ...divide both sides by 3
y = -2/3x + 490

In y = mx + b form (slope intercept form), the slope will be in the m position and the y int will be in the b position

y = -2/3x + 490
y = mx + b

as u can see, the number in the m position (the slope) = -2/3
and the number in the b position (the y int) = 490 or (0,490)

Yanka [14]4 years ago

7 0

Answer:

Slope is -2/3.

y-intercept is 490.

Step-by-step explanation:

Slope intercept form of a line is y = mx + c

Where, m is the slope of the line,

Here, the given equation is,

2x + 3y = 1,470,

By subtraction property of equality,

3y = -2x + 1470

By the division property of equality,

$\implies y = -\frac{2}{3}x + 490$

By comparing,

$m = -\frac{2}{3}$

Thus, the slope of the given line is $-\frac{2}{3}$ ,

For y-intercept, x = 0,

$y=-\frac{2}{3}(0) + 490$

$\implies y = 490$

y-intercept of the line is 490.

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Answer:

The perimeter of polygon ABCD, to the nearest thousandth units is

22.227 units

The perimeter of polygon ABCD', to the nearest thousandth, would be 20.980 units

The area of polygon ABCD' is 19.5 units²

Step-by-step explanation:

The coordinates forming the polygon are

A (-4,-1), B(-2,3), C(2,2), and D(4,-3)

The perimeter then is given by the sum of the length of the sides as follows;

Length of line between two X and Y points distance, xi and yj apart is

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Therefore, the length between points AB is

length AB = $\sqrt{(-4 - (-2))^2+(-1-3)^2}$

= $\sqrt{(-4 +2)^2+(-4)^2} = \sqrt{-2^2+-4^2} = \sqrt{20}$ = 4.472 units

Similarly, length BC is given by

Length BC = $\sqrt{(-4)^2+1^2} = \sqrt{17}$ = 4.123 units

Length CD = $\sqrt{(-2)^2+5^2} = \sqrt{29}$ = 5.385 units

Length DA = $\sqrt{(8)^2+(-2)^2} = \sqrt{68}$ = 8.246 units

The perimeter is equal to;

length AB + Length BC + Length CD + Length DA

= 4.472 + 4.123 + 5.385 + 8.246 = 22.227 units

If the point D is moved up 2 units and left 1 unit we have

D' = x-1, y+2 where x and y are the coordinates of point D

D(4, -3) → D'((4-1), (-3+2)) = D'(3, -1)

The length D'A = $\sqrt{(7)^2+(0)^2} = \sqrt{49}$ =7 units

The perimeter of polygon ABCD'

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= 4.472 + 4.123 + 5.385 + 7 = 20.980 units.

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$S_{\bigtriangleup}$ = $(\frac{1}{2})|x_1y_2+x_2y_3+x_3y_1-x_1y_3-x_2y_1-x_3y_2|$

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B(-2,3)

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