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### Point Slope Form of an Equation

- The
*point-slope form*of a linear equation is an equation of the form y – y_{1}= m(x – x_{1}), where m is the slope of the graph and the point (x_{1}, y_{1}) is a point that lies on the graph. - If you are given a point that lies on a line and the slope of the line, you can immediately write the equation in point-slope form.
- If you are given two points that lie on a line, first find the slope using the formula for the slope, then use either point to write the equation in point-slope form.
- You now have 3 forms of a linear equation: point-slope, slope-intercept, and standard form. You can convert from one form to the other two forms using algebraic transformations of the given equation.

### Point Slope Form of an Equation

A line has a slope of - 4 and passes through the point ( - 4, - 3).

Find the equation of this line in point slope form.

Find the equation of this line in point slope form.

- y − y
_{1}= m(x − x_{1}) - y − ( − 3) = m[x − ( − 3)]
- y + 3 = m(x + 3)

y + 3 = − 4(x + 3)

A line has a slope of - 7 and passes through the point (11, - 1).

Find the equation of this line in point slope form.

Find the equation of this line in point slope form.

- y − y
_{1}= m(x − x_{1}) - y − ( − 1) = − 7(x − 11)

y + 1 = − 7(x − 11)

A line has a slope of - 8 and passes through the point ( - 14,10).

Find the equation of this line in point slope form.

Find the equation of this line in point slope form.

- y − y
_{1}= m(x − x_{1}) - y − 10 = − 8[x − ( − 14)]

y − 10 = − 8(x + 14)

A horizontal line passes through the point (5,3). Find the equation of this line in point slope form.

- slope = 0 for a horizontal line

m = 0 - y − y
_{1}= m(x − x_{1})

y − 3 = 0(x − 5)

A horizontal line passes through the point ( - 12, - 13). Find the equation of this line in point slope form.

- slope = 0 for a horizontal line

m = 0 - y − y
_{1}= m(x − x_{1}) - y − ( − 13) = 0[x − ( − 12)]

y + 13 = 0(x + 12)

The equation of a line is

y − 5 = [1/5](x + 3)

Find the equation of this line in slope intercept form.

y − 5 = [1/5](x + 3)

Find the equation of this line in slope intercept form.

- y − 5 = [1/5](x + 3)
- 5(y − 5) = [ [1/5](x + 3) ]5
- 5y − 25 = 1(x + 3)
- 5y − 25 = x + 3
- 5y − 25 + 25 = x + 3 + 25
- 5y = x + 28
- y = [(x + 28)/5]

y = [1/5]x + [28/5]

The equation of a line is

y + 10 = [7/30](x − 2)

Find the equation of this line in slope intercept form.

y + 10 = [7/30](x − 2)

Find the equation of this line in slope intercept form.

- y + 10 = [7/30](x − 2)
- 30(y + 10) = [ [7/30](x − 2) ]30
- 30y + 300 = 7(x − 2)
- 30y + 300 = 7x − 14
- 30y = 7x − 314
- y = [(7x − 314)/30]
- y = [7/30]x − [314/30]

y = [7/30]x − [157/15]

The equation of a line is y + 12 = [5/6](x + 9)

Find the equation of this line in slope intercept form.

Find the equation of this line in slope intercept form.

- y + 12 = [5/6](x + 9)
- 6(y + 12) = [ [5/6](x + 9)]6
- 6y + 72 = 5(x + 9)
- 6y + 72 = 5x + 45
- 6y = 5x − 27

y = [(5x − 27)/6]

A line passes through the points (7,9) and (2,5). Find the equation of this line in point slope form.

- m = [(y
_{2}− y_{1})/(x_{2}− x_{1})] - m = [(5 − 9)/(2 − 7)]
- m = [( − 4)/( − 5)]
- m = [4/5]
- y − y
_{1}= m(x − x_{1})

y − 9 = [4/5](x − 7)

A line passes through the points ( - 1,3) and ( - 7, - 11). Find the equation of this line in point slope form.

- m = [(y
_{2}− y_{1})/(x_{2}− x_{1})] - m = [( − 11 − 3)/( − 7 − ( − 1))]
- m = [( − 14)/( − 6)]
- m = [14/6] = [7/3]
- y − y
_{1}= m(x − x_{1}) - y − 3 = [7/3][x − ( − 1)]

y − 3 = [7/3](x + 1)

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.

Answer

### Point Slope Form of an Equation

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

- Intro 0:00
- Point Slope Form 0:07
- Manipulating to Other Forms
- m (Slope), x1 y1 (Point)
- Example 1: Point Slope Form Equation 1:03
- Example 2: Point Slope Form Equation 2:50
- Example 3: Point Slope Form Equation 4:18
- Example 4: Point Slope Form Equation 6:50

0 answers

Post by Kapil Patel on February 14, 2017

using the given conditions to write an equation for the line in point slope form and slope-intercept form passing through (-4,13)and (1,-2).

1 answer

Last reply by: Dr Carleen Eaton

Tue Jun 18, 2013 6:38 PM

Post by Taylor Wright on June 18, 2013

Wouldn't it be easier to just distribute the 2/3 to the (x+4) and then add 3 to both sides?

1 answer

Last reply by: Dr Carleen Eaton

Fri May 17, 2013 7:18 PM

Post by Erika Porter on May 17, 2013

Dr. Eaton,

On example 3, you multiplied y-3=2/3(x+4)by 3 giving you:

3(y-3)=[2/3(x+4)]3

which then gave you 3y-9=2(x+4).

My question is: Why was the (x+4) not multiplied by 3 as well?

However, when I worked the problem, I substituted the known values for x (-4),y(3), and m(2/3) into the slope intercept form to solve for b.

3=(2/3)(-4)+b

solving for b...b=17/3

then...putting into slope intercept form I came up with y=2/3x+17/3 which is the same answer as you.

I am perplexed.

thanks,

Jake

0 answers

Post by S A A Mazeed Sumon on April 29, 2010

Did Not Close The First Bracket for X....