a. Use the point-slope formula to find the equation of the line that goes through the point (5,3) and has slope .
(x1,y1)=(5,3)Let (x1,y1) be the given pointm=0m is the given slopey−y1=m(x−x1)Point slope formulay−3=0(x−5)Substitute 5 for x, 3 for y and 0 for my−3=0Rewrite the equation in the form y=mx+by=3Add 3
b. Does your answer to part a simplify to the equation of a horizontal line through (0,b)?
Yes because if m is equal to zero in the point slope form... then the expression written in the right side of the equation will be zero as well. What is left is the y coordinate of the point that makes the equation a horizontal line.
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