# How do you the equation of the line that passes through point (4,2) and (6,6)?

##### 2 Answers

#### Explanation:

The slope of the line through

is

The slope-point form for a line

with slope

through the point

is

Using

and the previously determined

The slope-point form for the required line is

This could easily be converted into slope-point form as

or into standard form as

#### Explanation:

The equation of a line in

#color(blue)"slope-intercept form"# is

#color(red)(bar(ul(|color(white)(a/a)color(black)(y=mx+b)color(white)(a/a)|)))#

where m represents the slope and b, the y-intercept.To calcuate m, use the

#color(blue)"gradient formula"#

#color(red)(bar(ul(|color(white)(a/a)color(black)(m=(y_2-y_1)/(x_2-x_1))color(white)(a/a)|)))#

where# (x_1,y_1)" and " (x_2,y_2)" are 2 coordinate points"# The 2 points here are (4 ,2) and (6 ,6)

let

# (x_1,y_1)=(4,2)" and " (x_2,y_2)=(6,6)#

#rArrm=(6-2)/(6-4)=4/2=2# Thus partial equation is :

#y=2x+b# To find b, substitute either of the 2 given points into the partial equation and solve for b.

Using (4 ,2) :

#(2xx4)+b=2rArrb=2-8=-6#

#rArry=2x-6" is the equation of the line"#