Two points whose coordinates are #(4, 17)# and #(2, a)# determine a line whose slope is #6#. What is the value of #a#?

1 Answer
Jim G.
Apr 14, 2018

#a=5#

Explanation:

#"to calculate the slope m use the "color(blue)"gradient formula"#

#•color(white)(x)m=(y_2-y_1)/(x_2-x_1)#

#"let "(x_1,y_1)=(4,17)" and "(x_2,y_2)=(2,a)#

#rArrm=(a-17)/(2-4)=(a-17)/(-2)#

#"we are given that "m=6#

#"thus equate the two and solve for a"#

#rArr(a-17)/(-2)=6#

#"multiply both sides by "-2#

#cancel(-2)xx(a-17)/cancel(-2)=-2xx6#

#rArra-17=-12#

#"add 17 to both sides"#

#acancel(-17)cancel(+17)=-12+17#

#rArra=5#

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