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# Ant 101

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In the graph below, each grid line counts as one unit. The line shown below passes through the point $$(1001,n)$$ (not shown on graph). Find n .

ant101  Mar 24, 2017
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#1
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Note that the line passes through the points (0,3)  and (7,7)

So.....the slope if this line  is    [7 -3 ] / [7 - 0]   =   4/7

And  using the point  (0,3)  the equation of the line is

y  = (4/7)x  + 3

And when x  =  1001

y  = (4/7)(1001) +  3     =  573

So    (1001, n)   =   (1001, 573)

CPhill  Mar 24, 2017
#2
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In the graph below, each grid line counts as one unit.

The line shown below passes through the point  (not shown on graph).

Find n .

The line passes through the points (0,3)  and (-7,-1)

$$\begin{array}{|rcll|} \hline \text{slope } = \frac{3-(-1)}{0-(-7)} &=& \frac{n-3}{1001-0} \\ \frac{3-(-1)}{0-(-7)} &=& \frac{n-3}{1001-0} \\ \frac{4}{7} &=& \frac{n-3}{1001} \\ 1001\cdot \frac{4}{7} &=& n-3 \\ 3+ 1001\cdot \frac{4}{7} &=& n \\ \mathbf{575} & \mathbf{=} & \mathbf{n} \\ \hline \end{array}$$

heureka  Mar 24, 2017

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