$\bf ~~~~~~~~~~~~\textit{internal division of a line segment}\\\\\\A(1,4)\qquad B(6,2)\qquad\qquad \stackrel{\textit{ratio from A to B}}{2:3}\\\\\\ \cfrac{A\underline{C}}{\underline{C} B} = \cfrac{2}{3}\implies \cfrac{A}{B} = \cfrac{2}{3}\implies 3A=2B\implies 3(1,4)=2(6,2)\\\\[-0.35em]~\dotfill\\\\C=\left(\frac{\textit{sum of "x" values}}{\textit{sum of ratios}}\quad ,\quad \frac{\textit{sum of "y" values}}{\textit{sum of ratios}}\right)\\\\[-0.35em]~\dotfill$

$\bf C=\left(\cfrac{(3\cdot 1)+(2\cdot 6)}{2+3}\quad ,\quad \cfrac{(3\cdot 4)+(2\cdot 2)}{2+3}\right)\implies C=\left(\cfrac{3+12}{5}~,~\cfrac{12+4}{5} \right)\\\\\\C=\left( \cfrac{15}{5}~,~\cfrac{16}{5} \right)\implies C=\left( 3~,~3\frac{1}{5} \right)$

6 0

3 years ago

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A line goes through the points (9,8) and (4,-12). What is the slope of the line? Show your work Write the equation of the line i

RoseWind [281]

The slope of the line is 4

The point slope form of the line can be written as (y - 8) = 4(x - 9)

The slope intercept form of the line is y = 4x - 28

In order to find the slope you will need to use the formula for slope. It is included below.

m(slope) = (y2 - y1)/(x2 - x1)

m = (8 - -12)/(9 - 4)

m = (8 + 12)/(9 - 4)

m = 20/5

m = 4

Now that we have the slope, we can plug it into point slope form along with one of the points.

(y - y1) = m(x - x1)

(y - 8) = 4(x - 9)

Now to get to the slope-intercept form of the line, we can simply manipulate the point-slope form until it is in y = mx + b

(y - 8) = 4(x - 9) ----> Distribute the 4

y - 8 = 4x - 36 -----> Add 8 to both sides

y = 4x - 28

5 0

3 years ago

-8+h=3 can y’all help me

photoshop1234 [79]

Answer: 5

Step-by-step explanation:

If you do -8-3 you’d get 5

4 0

2 years ago

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