Question

Describe what you know about the graph of a line represented by the equation y - 3 = -2/3(x +4)

Answer 1

see the explanation

Explanation:

we have

`y-3=-(2)/(3)(x+4)`

This is the equation of a line in point slope form

The slope is negative and equal to
`m=-(2)/(3)`

The line passes through the point (-4,3)

The y-intercept (value of y when the value of x is equal to zero) is

For x=0

`y-3=-(2)/(3)(0+4)`

`y-3=-(8)/(3)`

`y=-(8)/(3)+3`

`y=(1)/(3)`

The y-intercept is
`(0,(1)/(3))`

The x-intercept (value of x when the value of y is equal to zero) is

For y=0

`0-3=-(2)/(3)(x+4)`

`(9)/(2)=(x+4)`

`x=(9)/(2)-4`

`x=(1)/(2)`

The x-intercept is
`(0.5,0)`

see the attached figure to better understand the problem