How do you write an equation in slope intercept form of a line containing the points (3,7) , (6,8)?
1 Answer
Explanation:
The equation of a line in
#color(blue)"slope-intercept form"# is.
#color(red)(|bar(ul(color(white)(a/a)color(black)(y=mx+b)color(white)(a/a)|)))#
where m represents the slope and b, the y-intercept.We require to find m and b. To calculate m use the
#color(blue)"gradient formula"#
#color(red)(|bar(ul(color(white)(a/a)color(black)(m=(y_2-y_1)/(x_2-x_1))color(white)(a/a)|)))#
where# (x_1,y_1)" and " (x_2,y_2)" are 2 coordinate points"# The 2 points here are (3 ,7) and (6 ,8)
let
# (x_1,y_1)=(3,7)" and " (x_2,y_2)=(6,8)#
#rArrm=(8-7)/(6-3)=1/3# We can write the partial equation as
#y=1/3x+b# To find b, substitute the coordinates of either of the 2 points into the partial equation and solve for b.
Using the point (3 ,7) that is x = 3 and y = 7
#rArr(1/3xx3)+b=7rArr1+b=7rArrb=6# Thus
#y=1/3x+6" is equation in slope-intercept form"#
