a) Find an equation of the line passing through (-4, 2) and (3, 6).
b) Find the slope of any line perpendicular to your answer from a)
| Foundations
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1) How do you find the slope of a line through points  and Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle (x_{2},y_{2})}
?
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| 2) What is the equation of a line?
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3) How do you find the slope of a line perpendicular to a line  ?
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| Answer:
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1) The slope is given by  .
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2) The equation of a line is  where is a point on the line.
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3) The slope is given by  where  is the slope of the line .
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Solution:
| Step 1:
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| Using the above equation, the slope is equal to Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle m={\frac {6-2}{3-(-4)}}={\frac {4}{7}}}
.
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| Step 2:
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The equation of the line is  . Solving for ,
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| we get Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle y={\frac {4}{7}}x+{\frac {30}{7}}}
.
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| Step 3:
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| The slope of any line perpendicular to the line in Step 2 is Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle -{\frac {1}{({\frac {4}{7}})}}=-{\frac {7}{4}}}
.
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| Final Answer:
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| The slope is Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle {\frac {4}{7}}}
, the equation of the line is Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle y={\frac {4}{7}}x+{\frac {30}{7}}}
, and
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the slope of any line perpendicular to this line is  .
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