Write Equations from Slope and Point

4.3- Writing equation in point slope form

By: Anshuman Sharma

Vocabulary and Formula:

 

• Point-Slope form: An equation of a line can be written in point-slope form when given the coordinates of one known point on a line and the slope of that line.

• Point slope form formula: y-y1=m(x-x1)

• slope-Intercept form: y=mx+b

• Standard Form: Ax+By=C

Example 1:

Write the equation in point-slope form for the line that passes through the given point with the slope provided.

(-2,5), slope -6

y-y1=m(x-x1)

y-5=-6(x-(-2)) Sustitute

y-5=-6(x+2) Solve

y-5=-6x-12

Example 2:

Write an equation in standard form.

*Remember the value for A cannot be a negative or a Fraction.
y+2=7/8(x-3)  This has a slope of fraction so first we multiply the   8(y+2=7/8(x-3))         whole equation by the denominator.

8y+16=7(x-3)
8y+16=7x-21
    -16      -16
8y=7x-37
7x-27=8y
7y-8y=27

Write the equation in standard form:

This is an example with a non-fraction slope:

y-10=2(x-8)

y-10=2x-16

+10 +10

y=2x-6

2x-6=y

2x-y=6

Write an equation in standard form:

This is an example of writing standard form with a negative slope.

y+7=-5(x+3)

y+7=-5x-15

-7 -7

y=-5x-22

+5x +5x

5x+y=-22

Example 3:

Write an equation in slope-intercept form:

y-10=4(x+6)

y-10=4x+24

+10 +10

y=4x+34

Multiple Choice

What is the standard form for the following equation:

y-9=-6(x+9)

• 6x-y=-45

• 6x+y=-45

• -6x-y=45

• 9x-10y=43

Multiple Choice

Write the equation in slope-intercept form:

y-11=3(x+4)

• y=-3x-1

• No Solution

• y=3x+1

• y=3x

Multiple Choice

Write an equation in point-slope form for the line that passes through each point with the given slope:

(-6,0), horizontal line

• y=0

• y-0=-6

• Undefined

• y=1

Word problem Example 1:

Movie rentals: The number of copies of a movie rented at a video store decreased at a constant rate of 5 copies per week. The 6th week after the movie was released, 4 copies were rented. How many copies were rented during the second week?

The slope is -5 and the point in (6,4)

Equation: y-4=-5(x-6) Substitute 2 for x

y-4=-5(2-6)

y-4=-10+30

y-4=20

+4 +4

y=24

There were 24 movies rented the second week.

Write an equation in point-slope form for each line.

y-y1=m(x-x1)

y-(-1)=3/2(x-(-4))

y+1=3/2(x+4)

!!Challenge Problem!!

Write an equation in point-slope form for the line that passes through the points (f,g) and (h,j)

y-y1=m(x-x1)
y-g= $\frac{j-g}{h-f}$  (x-f)