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3 years ago

What is the image point of (-4, 8) after a translation right 4 units and up 2 units?

Mathematics

1 answer:

Vitek1552 [10]3 years ago

4 0

Given:

Point = ( -4,8).

To find:

The image point of (-4, 8) after a translation right 4 units and up 2 units.

Solution:

We know that, if a figure translated 4 units right and 2 units up, then the rule of translation is

$(x,y)\to (x+4,y+2)$

The point is (-4,8).

Putting x=-4 and y=8, we get

$(-4,2)\to (-4+4,8+2)$

$(-4,2)\to (0,10)$

Therefore, the image of point (-4,8) is (0,10).

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A house sells for 2.95×10^5 dollars. Write this number in standard form.

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Step-by-step explanation:

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8 0

3 years ago

1. What is an equation for the line with slope 2/3 and y-intercept 9?

Monica [59]

Question 1:

The generic equation of the line is given by:
$y = mx + b
$
Where,
m: slope of the line
b: cutting point with the y axis
Substituting values we have:
$y = \frac{2}3}x + 9
$
Answer:
an equation for the line with slope 2/3 and y-intercept is:
$y = \frac{2}3}x + 9$

Question 2:

The standard equation of the line is given by:
$y-yo = m (x-xo)
$
Where,
m: slope of the line
(xo, yo): ordered pair that belongs to the line
The slope of the line is:
$m = \frac{y2-y1}{x2-x1}$
Substituting values:
$m = \frac{1-(-3)}{3-1}$
$m = \frac{1+3}{3-1}$
$m = \frac{4}{2}$
$m = 2
$
We choose an ordered pair:
$(xo, yo) = (3, 1)
$
Substituting values:
$y-1 = 2 (x-3)
$
Rewriting:
$y = 2x - 6 + 1

y = 2x - 5$
Answer:
An equation in slope-intercept form for the line that passes through the points (1, -3) and (3,1) is:
$y = 2x - 5
$

Question 3:

For this case, since the variation is direct, then we have an equation of the form:
$y = kx
$ Where,
k: constant of variation.
We then have the following equation:
$-4y = 8x
$ Rewriting we have:
$y = \frac{8}{-4}x
$
$y = -2x
$ Therefore, the constate of variation is given by:
$k = -2
$
Answer:
the constant of variation is:
$k = -2$

Question 4:

For this case, since the variation is direct, then we have an equation of the form:
$y = kx
$ Where,
k: constant of variation.
We must find the constant k, for this we use the following data:
y = 24 when x = 8
Substituting values:
$24 = k8
$ Clearing k we have:
$k = \frac{24}{8} 
$
$k = 3
$
Therefore, the equation is:
$y = 3x
$ Thus, substituting x = 10 we have that the value of y is given by:
$y = 3 (10)

y = 30$ Answer:
the value of y when x = 10 is:
$y = 30$