Equations of a Line

Question 2

Find the equation of the line passing through the points
( 12, 5 ) and ( 14, 4 ). Give your answer in slope-intercept form.

Solution

To find the equation of the line, you need to determine the slope of the line. To do this, use the slope formula. This will give you,

   m = ( y2 - y1 ) / ( x2 - x1 )
 m
= ( 4 - 5 ) / ( 14 - 12 )
 m = -1/2
 

.Now that you have the slope of the line, plug it and a point on the line into the slope-intercept formula and solve for b.

   y = mx + b
 y = ( -1/2 )x + b
 ( 5 ) = ( -1/2 )( 12 ) + b
 5 + 6 = b
 b = 11
 

Finally, plug in your values of m and b into the slope-intercept formula. Therefore, your final answer will be,

   y = ( -1/2 )x + 11  


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