We are given the y-intercept. How can the changes in the dependent and independent variables give us the slope?
Slope: -2/5
y-intercept: 4
x-intercept: 10 Graph:
Practice makes perfect
We will use the given information to determine some features of the function, starting with the slope.
Slope
Consider that the slope of a line represents 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 5 units.
slope=-2/5 ⇔ slope=-2/5
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. We are given this value.
h( 0)= 4
The y-intercept is 4, so the graph intercepts the y-axis at the point ( 0, 4).
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 (10,0), so the x-intercept is 10.
