# 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