You can use point-slope form. How does the balance change over the weeks?
Equation: y=50x+100 Example interpretation: The balance increases by $50 each week.
Practice makes perfect
We are given a graph showing how the balance in a bank account changes over time.
Since we are given a slope and point on the line, it will be most convenient to use point-slope form.
Equations in this form follow a specific format.
y- y_1= m(x- x_1)
In this form, m is the slope of the line and ( x_1, y_1) is a point on the line. We can identify these values using the graph. Let's start with the slope.
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 (4,300) from the point (2,200) requires that we move 2 steps horizontally in the positive direction and 100 steps vertically in the positive direction.
rise/run=100/2=50 ⇔ m= 50
The slope of 50 tells us that the balance increases by $50 each week.
Writing the Equation
Now that we know that the slope of the line is 50, we can write the equation of the line in point-slope form. We can use either of the given points as (x_1,y_1) in our equation. Let's use ( 4, 300).
While this is a valid format for the equation of the line, we can rewrite it in the slope-intercept form so that we can have the unique equation for the line.
