How do you write the equation of a line given (6,1) (-3,-2)?
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.To obtain the equation ,we require to find m and b.
m can be calculated using 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 points"# let
# (x_1,y_1)=(6,1)" and " (x_2,y_2)=(-3,-2)#
#rArrm=(-2-1)/(-3-6)=(-3)/(-9)=1/3# Partial equation is
#y=1/3x+b# To find b , substitute one of the 2 given points into the partial equation, say (-3 ,-2)
x = -3 , y = -2 gives.
#-2=(1/3xx-3)+b→-2=-1+b→b=-1#
#rArry=1/3x-1" is the equation of the line"#
graph{1/3x-1 [-10, 10, -5, 5]}
