PLEASE HELP THIS IS OVERDUE!!

Find the equation of a line perpendicular to y - 12 = 2x – 8 that passes through the point (2, 3). (answer in slope-intercept fo

Alla [95]

Answer:

$\displaystyle y=-\frac{1}{2}x+4$

Step-by-step explanation:

<u>Equation of a Line</u>

We can find the equation of a line by using two sets of data. It can be a pair of ordered pairs, or the slope and a point, or the slope and the y-intercept, or many other combinations of appropriate data.

We are given a line

$y - 12 = 2x -8$

And are required to find a line perpendicular to that line. Let's find the slope of the given line. Solving for y

$y = 2x +4$

The coefficient of the x is the slope

$m=2$

The slope of the perpendicular line is the negative reciprocal of m, thus

$\displaystyle m'=-\frac{1}{2}$

We know the second line passes through (2,3). That is enough information to find the second equation:

$y-y_o=m'(x-x_o)$

$\displaystyle y-3=-\frac{1}{2}(x-2)$

Operating

$\displaystyle y=-\frac{1}{2}(x-2)+3$

Simplifying

$\displaystyle y=-\frac{1}{2}x+4$

That is the equation in slope-intercept form. Intercept: y=4

8 0

3 years ago

Translate the shape A three squares right and one square down.

Alexus [3.1K]

Answer:

see explanation

Step-by-step explanation:

a shift of 3 squares right means add 3 to the x- coordinate

a shift of 1 square down means subtract 1 from the y- coordinate

translation rule is (x, y ) → (x + 3, y - 1 ) , then

(1, 1 ) → (1 + 3, 1 - 1 ) → (4, 0 )

(1, 4 ) → (1 + 3, 4 - 1 ) → (4, 3 )

(3, 1 ) → (3 + 3, 1 - 1 ) → (6, 0 )

6 0

2 years ago

Write an expression for the eighth partial sum of the series using summation notation

balandron [24]

Answer:

option B

Step-by-step explanation:

9/10 + 6/5 + 3/2...........

We find the difference between the terms

$\frac{6}{5} - \frac{9}{10}$

$\frac{12}{10} - \frac{9}{10} = \frac{3}{10}$

We will get the same difference when we subtract consecutive terms.

so , d= 3/10, a= 9/10

we find the formula for nth term

a_n = a+(n-1) d

$a_n = \frac{9}{10} + (n-1)\frac{3}{10}$

$a_n = \frac{9}{10} +\frac{3}{10}n-\frac{3}{10}$

$a_n = \frac{6}{10} +\frac{3}{10}n$

$a_n = \frac{3}{5} +\frac{3}{10}n$

we need to find eighth partial sum so we take n=1 to 8

sum of 8 terms ( $\frac{3}{5} +\frac{3}{10}n$ )

So option B is correct

4 0

3 years ago

What is 4x +12=20 proof

dimulka [17.4K]

4x+12=20
-12 -12
——————
4x=8
divide by 4 on both sides
x=2

3 0

3 years ago

A line passes through (2, −1) and (4, 5).

mash [69]

The answer to the first problem is the top left corner because it is the only one with a -3 y-intercept and that's in the problem

To find the answer of the second problem you find the slope of the two points with the formula y2-y1 divided by x2-x1 and you just plug it in so 5+1 (the minus signs cancel out and turn into positives) divided by 4-2 and which is 6/2 which is 3 is your slope. then you could plug this information into a point slope form using either point I'm just going to choose the one with no negatives so plugging this in would be y-5=3(x-4) then you distribute the 3 and that gives you y-5=3x-12 then
+5 +5 add five to both sides of the equation and get
y=3x-7 and then you can put that into standard form which would be -3x+y=-7 and your answer would be the second one.

6 0

3 years ago