Question

A linear function h models a relationship in which the dependent variable decreases 2 units for every 3 units the independent variable increases. Graph h when h(0)=2. Then identify the slope, y-intercept, and x-intercept of the graph.

Answer 1

Answer:

Slope=-2/3,  y-intercept=2, x-intercept=3

Step-by-step explanation:

Let the independent variable be x and dependent variable be y

y=h(x)

h is a linear function so it is represented in the general form of y=mx+c where

m is slope and c is the y-intercept.

Given "the dependent variable decreases 2 units for every 3 units the independent variable increases."

When x increases by 3, y decreases by 2

So the slope = rate of change of y / rate of change of x = -2/3

Given h(0)=2, h(0)=m(0)+c=2

c=2

Combining slope and y-intercept, y=-2/3*x+2

x-intercept is when y=0

0=-2/3*x+2

2/3*x=2

x=2*3/2=3

x-intercept=3

Answer 2

Answer:

y-intercept is (0,2)

slope is -2/3

x-intercept is (3,0)

Step-by-step explanation:

h is linear fn

so y=h(x)=mx+C

y-intercept=h(0)=2=C

the dependent variable decreases 2 units for every 3 units the independent variable increases

so slope=independent var/dependent var=-2/3

y=-2/3x+2

x-intercept=h(x)=0

0=-2/3x+2

2/3x=2

x=3