algebra class work

Question

A linear function  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 

Answer 1

h is the dependent variable, let t be the independent variable, such as time

The slope = -2/3,

h(0)=2 which is the "y-intercept" or in this case the "h intercept:

h(t) = (-2/3)t + 2. It's a straight line downward sloping with slope -2/3, going through the point (0,2) This is the slope intercept form of a linear equation. In more general terms, y=mx+b where m= slope, b= y intercept, y is the dependent variable and x is the independent variable.

You could also set h=0 and solve for the t intercept on the horizontal axis 0=(-2/3)t+2 or

(-2/3)t=-2

t = -2(3/-2) = 3 The point (3,0) is the t intercept where the line crosses the horizontal axis.

Just connect those two points with a straight line, (3,0) and (0,2) That line is the graph of h(t)=(-2/3)t+2

Answer 2

This would have the form y=mx + b, resulting in h(x) = -(2/3)x + 2

(I don't know how to insert a graph. It got rejected for size regardless of how small I made it.)