What is the equation of the line passing through (-3,-2 ) and (1, -5)?
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 (-3 ,-2) and (1 ,-5)
let
# (x_1,y_1)=(-3,-2)" and " (x_2,y_2)=(1,-5)#
#rArrm=(-5-(-2))/(1-(-3))=(-3)/4=-3/4# We can use either of the points (-3 ,-2), (1 ,-5) as the point on the line since the line passes through both of them.
#"Using " (x_1,y_1)=(1,-5)" and "m=-3/4# Substitute these values into the equation.
#y-(-5)=-3/4(x-1)#
#rArry+5=-3/4(x-1)larrcolor(red)" in point-slope form"# Distributing and simplifying gives an alternative version of the equation.
#y+5=-3/4x+3/4#
#rArry=-3/4x+3/4-5#
#rArry=-3/4x-17/4larrcolor(red)"in slope-intercept form"#
