# How do you write out the equation of the line passing through #(1,5) (6,15)#?

##### 2 Answers

#### Explanation:

Use point-slope and slope formula.

We first need to find the slope by finding the change in y over the change in x. This would be

Now if we look at point slope formula, it is

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#### Explanation:

## Apply slope formula

- use formula
#m=(y_2-y_1)/(x_2-x_1)# given two points#(x_1,y_1)# and#(x_2,y_2)# (doesn't matter which one comes first)

the slope you get should be#\color(olive)(m)=10/5=2/1=\color(olive)(2)#

## Apply point-slope formula

- now plug-in one of the points for the formula
#y-y_1=m(x-x_1)# ,

which will now become#y-y_1=\color(olive)(2)(x-x_1)# .

here,#\color(indianred){(x_1,y_1)}# can be either of the points.

for easier explanation, used#\color(indianred){(1,5)}#

## Working it out

step A

step B

step C

step D

- therefore the equation is:

#\color{cornflowerblue}{y=2x+3}#