# What is the equation of the line passing through #(1,3), (4,6)#?

##### 2 Answers

#### Explanation:

#"the equation of a line in "color(blue)"slope-intercept form"# is.

#•color(white)(x)y=mx+b#

#"where m is the slope and b 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)=(1,3)" and "(x_2,y_2)=(4,6)#

#rArrm=(6-3)/(4-1)=3/3=1#

#rArry=x+blarrcolor(blue)"is the partial equation"#

#"to find b substitute either of the 2 given points into"#

#"the partial equation"#

#"using "(1,3)" then"#

#3=1+brArrb=3-1=2#

#rArry=x+2larrcolor(red)"is the equation of the line"#

#### Explanation:

First, we must know what an equation of a line looks like. We write the equation in slope-intercept form:

(The

Next, find the slope (

Next, find the y-intercept (

-OR-

Now, we can write the full equation of the line:

(We do not need to put a