Without calculating the slope, determine which of the following lines have a positive slope , and which have
negative slope ,
The line through and
The line through and
The line through and .

Question

Without calculating the slope, determine which of the following lines have a positive slope , and which have
negative slope ,
The line through and
The line through and
The line through and .

Ask by Pope Boyd. in South Africa

Mar 26,2025

UpStudy AI · Accepted Answer

1. For the line through $$ (-1, 3) $$ and $$ (-2, -1) $$:  
   - Order the points by $$ x $$: from $$-2$$ to $$-1$$ (increasing $$ x $$).  
   - At $$ x=-2 $$ the corresponding $$ y $$ is $$-1 $$, and at $$ x=-1 $$ it is $$ 3 $$.  
   - Since $$ y $$ increases from $$-1$$ to $$ 3 $$ as $$ x $$ increases, the slope is positive, i.e., $$ a>0 $$.

2. For the line through $$ (5, -2) $$ and $$ (3, 2) $$:  
   - Order the points by $$ x $$: from $$ x=3 $$ to $$ x=5 $$.  
   - At $$ x=3 $$ the corresponding $$ y $$ is $$ 2 $$, and at $$ x=5 $$ it is $$-2 $$.  
   - Here, $$ y $$ decreases from $$ 2 $$ to $$-2 $$ as $$ x $$ increases, so the slope is negative, i.e., $$ a<0 $$.

3. For the line through $$ (0, 1) $$ and $$ (-3, -6) $$:  
   - Order the points by $$ x $$: from $$ x=-3 $$ to $$ x=0 $$.  
   - At $$ x=-3 $$ the corresponding $$ y $$ is $$-6 $$, and at $$ x=0 $$ it is $$ 1 $$.  
   - As $$ x $$ increases, $$ y $$ increases from $$-6$$ to $$ 1 $$, thus the slope is positive, i.e., $$ a>0 $$.
1. The line through $$ (-1, 3) $$ and $$ (-2, -1) $$ has a positive slope. 2. The line through $$ (5, -2) $$ and $$ (3, 2) $$ has a negative slope. 3. The line through $$ (0, 1) $$ and $$ (-3, -6) $$ has a positive slope.

Without calculating the slope, determine which of the following lines have a positive slope , and which have
negative slope ,
The line through and
The line through and
The line through and .

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Without calculating the slope, determine which of the following lines have a positive slope , and which have
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