How do you write the slope intercept form of a line going through (1,3) and (3,7)?
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 slope and b, the y-intercept.We require to find m and b.
To calculate m use the
#color(blue)"gradient formula"#
#color(orange)"Reminder " 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),(x_2,y_2)" are 2 points on the line"# The 2 points here are (1 ,3) and (3 ,7)
let
# (x_1,y_1)=(1,3)" and " (x_2,y_2)=(3,7)#
#rArrm=(7-3)/(3-1)=4/2=2# We can now write the partial equation as y = 2x + b
To find b, substitute either of the 2 given points into the
partial equationUsing (1 ,3) that is x = 1 and y = 3
#3=(2xx1)+brArr3=2+brArrb=1#
#rArry=2x+1" is the equation in slope-intercept form"#
