What is the equation of the line that passes through (#5, -2)# and #(3, 4)#?
3 Answers
Explanation:
#"the equation of a line in "color(blue)"slope-intercept form"# is.
#•color(white)(x)y=mx+c#
#"where m is the slope and c the y-intercept"#
#"to calculate m use the "color(blue)"gradient formula"#
#•color(white)(x)m=(y_2-y_1)/(x_2-x_1)#
#"let "(x_1,y_1)=(5,-2)" and "(x_2,y_2)=(3,4)#
#m=(4-(-2))/(3-5)=6/(-2)=-3#
#y=-x+clarrcolor(blue)"is the partial equation"#
#"to find c substitute either of the 2 given points into"#
#"the partial equation"#
#"using "(3,4)" then"#
#4=-9+crArrc=4+9=13#
#y=-3x+13larrcolor(red)"is the equation of the line"#
The eqn. of
Explanation:
The eqn. of line passes through
#|(x,y,1),(x_1,y_1,1),(x_2,y_2,1)| =0#
We have , two points :
So, the eqn. of
#|(x,y,1),(5,-2,1),(3,4,1)| =0#
Expanding we get
Divding each term by
Explanation:
There is a useful formula which can be used to find the equation of a line if two points are known. It is based on the slope formula.
The points are