What is the equation in point-slope form of the line passing through (2, 5) and (–1, 8)?

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Answer 1 · 2015-05-30T07:27:37

#y = -x + 7#

First, we have to find the slope of the equation. To find the slope we have to do;

#"slope" = m = (y_2-y_1)/(x_2-x_1)#

For our question slope is;

#m = (8-5)/(-1-2) = 3/-3 = -1#

The equation of a line is;

#y=ax+b#

We should use one point to find the real equation. If we use #(2,5)# point;

#y= ax+b => 5=2a+b#

#a# is the slope of the equation, we found that as #-1#;

#5 = 2 * (-1) + b => 5= -2 +b => b=7#

So the equation of the line will be;

#y=ax+b => y= -x+7#

We can check if our equation is right or not with other given point;

#(-1,8) => y=-x+7 => 8=-(-1)+7 => 8=8#