How do you write an equation in slope intercept form of a line containing the coordinates (7,4) and (14,8)?
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.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 (7 ,4) and (14 ,8)
let
# (x_1,y_1)=(7,4)" and " (x_2,y_2)=(14,8)#
#rArrm=(8-4)/(14-7)=4/7# The equation can be partially written as
#y=4/7x+b# To find b, substitute either of the 2 given points into the equation and solve for b.
Using (7 ,4). That is x = 7 and y = 4
#rArr4=(4/7xx7)+brArr4=4+brArrb=0#
#rArry=4/7x" is the equation in slope-intercept form"#
