# How do you write in standard form an equation of the line with the slope -4 through the given point (2,2)?

##### 3 Answers

y

#### Explanation:

First off you have to know the standard form formula which is:

y

Plug in the slope and the points (x,y) to get b

y

2

2

Next, you add 8 to both sides to get b alone:

10

Plug your slope and b value into the standard formula

#### Explanation:

Let's start with the very definition of the slope of a line: take two points

From here, we have

To have the generic expression of the line, let's change this equation a little bit. Instead of having two fixed points

Plug your values:

From here, with a bit of algebra you get

**EDIT:**

as pointed out, we're not in the standard form yet. To achieve it, we must separate variables from "pure" numbers. Just move

#### Explanation:

#"the equation of a line in "color(blue)"standard form"# is.

#color(red)(bar(ul(|color(white)(2/2)color(black)(Ax+By=C)color(white)(2/2)|)))#

#"where A is a positive integer and B, C are integers"#

#"obtain the equation in "color(blue)"point-slope form ""and"#

#"rearrange into standard form"#

#â€¢color(white)(x)y-y_1=m(x-x_1)#

#"where m is the slope and "(x_1,y_1)" a point on the line"#

#"here "m=-4" and "(x_1,y_1)=(2,2)#

#rArry-2=-4(x-2)larrcolor(blue)"in point-slope form"#

#rArry-2=-4x+8#

#"add "4x" to both sides"#

#rArr4x+y-2=8#

#"add 2 to both sides"#

#rArr4x+y=10larrcolor(red)"in standard form"#