Answer:
Part 1) The slope is [tex]m=-2[/tex]
Part 2) The y-intercept is the point (0,-2)
Part 3) The x-intercept is the point (-1,0)
Step-by-step explanation:
step 1
Find the slope of the linear function
we know that
The dependent variable or output is the variable y
The independent variable or input is the variable x
we have that
The dependent variable decreases 4 units for every 2 units the independent variable increases
The slope m is
[tex]m=\frac{-4}{2}=-\frac{4}{2}= -2[/tex]
step 2
Find the y-intercept
we have the point (0,-2)
Remember that the y-intercept is the value of y when the value of x is equal to zero
so
The y-intercept is the point (0,-2)
step 3
Find out the equation of the linear function f in slope intercept form
[tex]f(x)=mx+b[/tex]
where
m is the slope
b is the y-coordinate of the y-intercept
we have
[tex]m=-2[/tex]
[tex]b=-2[/tex]
substitute
[tex]f(x)=-2x-2[/tex]
step 4
Find out the x-intercept
Remember that the x-intercept is the value of x when the value of y is equal to zero
For f(x)=0
[tex]0=-2x-2[/tex]
[tex]2x=-2[/tex]
[tex]x=-1[/tex]
The x-intercept is the point (-1,0)
see the attached figure to better understand the problem
