How do you write an equation given points (1,2), (3,8)?
1 Answer
Explanation:
The equation of a line in
#color(blue)"slope-intercept form"# is.
#color(red)(bar(ul(|color(white)(2/2)color(black)(y=mx+b)color(white)(2/2)|)))#
where m represents the gradient and b, the y-intercept.We have to find m and b.
To find m, use the
#color(blue)"gradient formula"#
#color(red)(bar(ul(|color(white)(2/2)color(black)(m=(y_2-y_1)/(x_2-x_1))color(white)(2/2)|)))#
where# (x_1,y_1)" and " (x_2,y_2)" are 2 coordinate points"# The 2 points here are (1 ,2) and (3 ,8)
let
# (x_1,y_1)=(1,2)" and " (x_2,y_2)=(3,8)#
#rArrm=(8-2)/(3-1)=6/2=3# We can write the partial equation as y = 3x + b
To find b, substitute either of the 2 given points into the
partial equation and solve for b.Using (1 ,2), that is x = 1 and y = 2.
#2=(3xx1)+brArr2=3+brArrb=-1#
#rArry=3x-1" is the equation"#
