Question

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

Answer 1

Answer:

see the explanation

Step-by-step explanation:

we have

$y-3=-\frac{2}{3}(x+4)$

This is the equation of a line in point slope form

The slope is negative and equal to $m=-\frac{2}{3}$

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

$y-3=-\frac{2}{3}(0+4)$

$y-3=-\frac{8}{3}$

$y=-\frac{8}{3}+3$

$y=\frac{1}{3}$

The y-intercept is $(0,\frac{1}{3})$

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

For y=0

$0-3=-\frac{2}{3}(x+4)$

$\frac{9}{2}=(x+4)$

$x=\frac{9}{2}-4$

$x=\frac{1}{2}$

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

see the attached figure to better understand the problem