What is the equation of the line that passes through the points (-3,5) (6,8)

1 answer:

6 0

$(\stackrel{x_1}{-3}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{8}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{8}-\stackrel{y1}{5}}}{\underset{run} {\underset{x_2}{6}-\underset{x_1}{(-3)}}}\implies \cfrac{3}{6+3}\implies \cfrac{3}{9}\implies \cfrac{1}{3}$

$\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{5}=\stackrel{m}{\cfrac{1}{3}}(x-\stackrel{x_1}{(-3)}) \\\\\\ y-5=\cfrac{1}{3}(x+3)\implies y-5=\cfrac{1}{3}x+1\implies y=\cfrac{1}{3}x+6$

You might be interested in

Which of these is the bet definition of an ellipse

Julli [10]

A regular oval shape, traced by a point moving in a plane so that the sum of its distances from two other points (the foci) is constant, or resulting when a cone is cut by an oblique plane which does not intersect the base.

7 0

4 years ago

97 points

rosijanka [135]

Remember:

The product of the sum of two perfect cubes:

a³ + b³ = (a + b)(a² - ab + b²)

The product of the difference of two perfect cubes:

a³ - b³ = (a - b)(a² + ab + b²)

----------------------------------------------------------------------------------------------------------------

Remember to follow PEMDAS.

(5c)(5c) = 25c²

(5c)(-2/3) = -10c/3

(2/3)(5c) = 10c/3

(2/3)(-2/3) = -4/9

25c²- 10c/3 + 10c/3 - 4/9

Combine like terms

25c² (-10c/3 + 10c/3) - 4/9

25c² - 4/9

25c² - 4/9 is your answer

hope this helps

4 0

4 years ago

Read 2 more answers

I don't get this. Can someone explain it better?

jarptica [38.1K]

Pick some number $a$ . Then multiply this by another number $r$ . Keep doing this and you generate a geometric sequence $a,ar,ar^2,ar^3,\ldots$ .

The 11th and 12th terms in this sequence are then $ar^{10}$ and $ar^{11}$ (because you get the 11th term after you multiply by $r$ 10 times, and the 12th term after 11 times).

The first term is, of course, $a$ . We're given $a=4$ and $r=\frac12$ . The sum of the 11th and 12th terms are then computed as shown in your picture.