point slope form

point slope form

How to write an equation of a line given 2 points

Write the equation of a line through the points (4, 0) and (-1, 10)

• Always start by finding the slope

• Slope

   $m\ =\frac{Y\ -\ Y}{X\ -\ X}$  

Multiple Choice

What is the slope of the line through the points (4, 0) and (-1, 10)?

• -10/3

• 3/10

• 2

• -2

Slope of line through (4,0) and (-1,10)

 $\frac{0-10}{4-\left(-1\right)}\ =\frac{-10}{5}=-2$  

Multiple Choice

If I want to write the equation in slope-intercept form Y=mx+b then I also need to know what?

• x-intercept

• y-intercept

• incline

y = -2x + b

• I can use the point (4 ,0) to find b

• 0 = -2(4) +b

Multiple Choice

Solve 0 = -2(4) +b

• b = -2

• b = -8

• b = 4

• b = 8

0 = -2(4) + b

0 = -8 + b

+8 +8

8 = b

Since m = -2 and b = 8 the equation is y=-2x+8

Point-Slope form: y-y₁=m(x-x₁)

is another way to find the equation of a line given 2 points

Reduce the slope -8/2 to -4 and use

y-y₁=m(x-x₁)

• Fill in -4 for the slope (m)

• Choose a point to fill in for (x₁ , y₁)

• We will use (4 ,2)

• y-2 = -4 (x-4)

Open Ended

What do you get when you distribute in the equation

y-2 = -4 (x-4)?

Multiple Choice

What should be done to the put the equation y-2 = -4x + 16

into slope-intercept form (y=mx+b)?

• Subtract 16 from both sides

• Subtract 2 from both sides

• Add 2 to both sides

• Divide both sides by -2

y=-4x + 18

You can get this answer using

Slope-Intercept form: y=mx+b or

Point-Slope form: y-y₁ = m (x-x₁)

Need more examples?

https://youtu.be/LtpXvUCrgrM

Multiple Choice

What should be done to the put the equation y-2 = -4x + 16

into slope-intercept form (y=mx+b)?

• Subtract 16 from both sides

• Subtract 2 from both sides

• Add 2 to both sides

• Divide both sides by -2