You are given the y-intercept. How can the changes in the dependent and independent variables give you the slope?
Slope: - 23 y-intercept: 2 x-intercept: 3 Graph:
Practice makes perfect
We will use the given information to determine some features of the function, starting with the slope.
Slope
Consider what slope represents. It is a change in the x- and y-values of the graph.
Slope=Change iny/Change inx
We are told that the dependent variable y decreases by 2 units every time the independent variable x increases by 3 units.
Slope=-2/3 ⇔ Slope=-2/3
y-intercept
Think of the point where the graph of an equation crosses the y-axis. The x-value of that ( x, y) coordinate pair is 0, and the y-value is the y-intercept. Let's look at the given value.
h( 0)= 2
Therefore the y-intercept is 2, so the graph intercepts the y-axis at the point ( 0, 2).
Graph
We now have enough information to graph the function. To start, plot the y-intercept and one other point using the slope we found above. By connecting these points with a line, we will form the graph of our equation.
x-intercept
Looking at our graph, we can also identify the x-intercept of this function.
The x-intercept of the function lies at the point (3,0), so the x-intercept is 3.
