How do you write an equation in slope-intercept form of the line that passes through the points (-2,-1) and (4,2)?
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 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),(x_2,y_2)" are 2 points on the line"# The 2 points here are (-2 ,-1) and (4 ,2)
let
# (x_1,y_1)=(-2,-1)" and " (x_2,y_2)=(4,2)#
#rArrm=(2-(-1))/(4-(-2))=3/6=1/2# We can write the partial equation as
#y=1/2x+b# To find b, substitute either of the 2 given points into the
partial equationChoosing the point (4 ,2) that is x = 4 and y = 2
#rArr2=(1/2xx4)+b#
#"Thus " 2=2+brArrb=0#
#rArry=1/2x" is the equation of the line"#
graph{1/2x [-10, 10, -5, 5]}
