Given `y=-0.2x+3 ` :
This is a linear function in slope-intercept form (y = mx + b, where m represents the slope and b represents the y-intercept.)
The slope is -0.2, or -1/5. Thus, as the independent (input) variable, x, increases, the dependent (output) variable, y, decreases. Graphically, for every 5 units we move to the right, the graph falls one unit.
The y-intercept is 3—this is where the graph crosses the y-axis. We can also think of 3 as the "initial" amount (i.e., the value of y when x is 0).
The graph of this function is a line, since the function is linear. We know that it is linear since the variable is in the first degree (x has an "implied" exponent of 1).
We can build a table of values to plot this line. Using convenient values for x, we find the following points on the graph: (0,3); (5,2); (10,1); and (15,0). From this last point, we find that the x-intercept is 15.
The graph of this equation looks like this:
We can also rewrite this function in other forms:
We can rewrite y = -(1/5)x + 3 as 5y = -x + 15, or x + 5y = 15, which is in standard form.
x + 5y - 15 = 0 is the equation in general form.
x/15 + y/3 = 1 is in the equation in intercept form.