Identify the y-intercept, then find another point that lies on the grid. How much does the tree grow over the years?
Equation: y=3/2x Example interpretation: The tree grows 3feet for every 2 years.
Practice makes perfect
We are given a graph showing how the height of a tree changes over time. Since we are given an y-intercept and a slope, it will be most convenient to use slope-intercept form.
Equations written in this form follow a specific format.
y= mx+b
In this form, m is the slope of the line and b is the y-intercept. We need to identify these values using the graph. Let's start with the y-intercept.
Finding the y-intercept
Observe the given graph.
We can see that the function intercepts the y-axis at (0, ). This means that the value of b is .
Finding and Interpreting the Slope
To identify the slope m, let's look at the rise and run of the graph.
Traveling to the point (4,6) from the y-intercept requires that we move 6 steps horizontally in the positive direction and 4 steps vertically in the positive direction.
rise/run=6/4=3/2 ⇔ m= 3/2
The slope of 32 tells us that the tree grows by 3feet every 2 years.
Writing the Equation
Now that we have the slope and the y-intercept, we can form our final equation.
y= mx+b [0.5em]
y= 3/2x+
⇔ y=3/2x
