Question

What is an equation of the line, in point-slope form, that passes through the given point and has the given slope?

point: (9, 3); slope: 4/9

Answer 1

choices are : .
y – 9 =4/9 (x + 3)

B.
y – 9 = 4/9 (x – 3)

C.
y + 3 =4/9 (x – 9)

D.
y – 3 = 4/9 (x – 9)ices are :

Answer 2

y = m x + b

Where:

m is the slope

b is the y-intercept

In tis case:

y = ( 4 / 9 ) x + b

You know coordinates of one point ( 9 , 3 )

Replace x = 9 , y = 3 in equation:

y = ( 4 / 9 ) x + b

3 = ( 4 / 9 ) ∙ 9 + b

3 = 4 + b

Subtact 4 to both sides

3 - 4 = 4 + b - 4

- 1 = b

b = - 1

So:

y = ( 4 / 9 ) x - 1

Answer 3

y – 3 = 4 / 9 ( x – 9 )

add 3 to both sides

y – 3 + 3 = 4 / 9 ( x – 9 ) + 3

y = ( 4 / 9 ) ∙ x – ( 4 / 9 ) ∙ 9 + 3

y = ( 4 / 9 ) x – 4 + 3

y = ( 4 / 9 ) x – 1

Answer D is correct.