Question in the image please help!!

35. For the following exercises, given each set of information, find a linear equation satisfying the conditions, if possible.

Montano1993 [528]

Answer:

The linear equation for the line which passes through the points given as (-2,8) and $(4,6), is written in the point-slope form as $y=-\frac{1}{3} x-\frac{26}{3}$ .

Step-by-step explanation:

A condition is given that a line passes through the points whose coordinates are (-2,8) and (4,6).

It is asked to find the linear equation which satisfies the given condition.

Step 1 of 3

Determine the slope of the line.

The points through which the line passes are given as (-2,8) and (4,6). Next, the formula for the slope is given as,

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Substitute $6 \& 8$ for $y_{2}$ and $y_{1}$ respectively, and 4&-2 for $x_{2}$ and $x_{1}$ respectively in the above formula. Then simplify to get the slope as follows, $m=\frac{6-8}{4-(-2)}$

$\begin{aligned}&m=\frac{-2}{6} \\&m=-\frac{1}{3}\end{aligned}$

Step 2 of 3

Write the linear equation in point-slope form.

A linear equation in point slope form is given as,

$y-y_{1}=m\left(x-x_{1}\right)$

Substitute $-\frac{1}{3}$ for m,-2 for $x_{1}$ , and 8 for $y_{1}$ in the above equation and simplify using the distributive property as follows, $y-8=-\frac{1}{3}(x-(-2))$\\ $y-8=-\frac{1}{3}(x+2)$\\ $y-8=-\frac{1}{3} x-\frac{2}{3}$$

Step 3 of 3

Simplify the equation further.

Add 8 on each side of the equation $y-8=-\frac{1}{3} x-\frac{2}{3}$ , and simplify as follows, $y-8+8=-\frac{1}{3} x-\frac{2}{3}+8$

$y=-\frac{1}{3} x-\frac{2+24}{3}$$\\ $$y=-\frac{1}{3} x-\frac{26}{3}$$

This is the required linear equation.

6 0

2 years ago

Which statements are true? Check all that apply.

mariarad [96]

Answer:

A, B, and C

Step-by-step explanation:

A) We can see if this is a horizontal line if its slope is 0. Slope is change in y divided by change in x, so: slope = $\frac{7-7}{3-(-2)} =\frac{0}{5} =0$ . Thus, this is a horizontal line and the statement is correct.

B) Any equation of the form x = k, where k is a constant, will always be a straight line. Let's see if it goes through (-8, 3) by plugging in the values of -8 in for x and 3 in for y in the equation.

Clearly, we don't have a y, so we just put in the -8 for the x: -8 = -8. Since this is a true statement, we know that x = -8 does go through (-8, 3). So, this is a true statement.

C) We can see if this is a vertical line if its slope is undefined (for example, if the denominator is 0, it's undefined). Slope = $\frac{5-(-7)}{0-0} =\frac{12}{0}$ = undefined. So, this is a vertical line and the statement is true.

D) As a basic fact, any point on a horizontal line will have the same y coordinate. However, their x coordinates may vary. Thus, the statement is false.

So, the answers are A, B, and C.

Hope this helps!

4 0

3 years ago

Read 2 more answers

The sum of two numbers is 98. their difference is 22. write a system of equations that describes this situation. solve by elimin

larisa [96]

Y+x=98
y-x=22

I'm going to use elimination.

y+x=98
y-x=22
-----------
2y+0x=120 SIMPLIFY 2y=120 SIMPLIFY y=60.

Substitute that into either equation and you get y=60 and x=38

Have a nice day! :)

6 0

3 years ago

Find the area of an equilateral triangle (regular 3-gon) with the given measurement.

olga nikolaevna [1]

The formula for finding the area of an equilateral triangle is

square root of 3 * (a^2/2)

a is the side length so in this case is 6

square root of 3 * (18)

the area is about 15.6

6 0

3 years ago

That picture is another question

erastovalidia [21]

Answer:

1. 3.82 miles

i dont have 2

3. 31

Step-by-step explanation:

5 0

3 years ago