What is the equation of the line that passes through (-1, -4) and (-2, 3)?
1 Answer
Explanation:
The equation of a line in
#color(blue)"point-slope form"# is.
#color(red)(bar(ul(|color(white)(2/2)color(black)(y-y_1=m(x-x_1))color(white)(2/2)|)))#
where m represents the slope and# (x_1,y_1)" a point on the line"# To calculate 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 coordinate points"# The 2 points here are (-1 ,-4) and (-2 ,3)
let
# (x_1,y_1)=(-1,-4)" and " (x_2,y_2)=(-2,3)#
#rArrm=(3-(-4))/(-2-(-1))=7/-1=-7# Using either of the 2 given points for
# (x_1,y_1)#
#"Using " (-1,-4)" and " m=-7" then"#
#y-(-4)=-7(x-(-1))#
#rArry+4=-7(x+1)larrcolor(red)"equation in point-slope form"# Distributing and simplifying this equation, gives us an alternative version for the equation of the line.
#y+4=-7x-7#
#rArry=-7x-11larrcolor(red)" equation in slope-intercept form"#
