Question

Question 1Thinking With Mathematical ModelsEarned vs. Saved$1,000$900$800$700$600Dollars Earned$500$400$300$200$1000$50 100 150 200 250Dollars SavedWrite an equation for the line relating dollars saved s to dollars earned e.

Answer 1

Writing a linear model from the graph

The equation of a line can be expressed in the slope-intercept form as:

y = mx + b

Where m is the slope of the line and b is the y-intercept

Suppose we know the line passes through points A(x1,y1) and B(x2,y2). The slope can be calculated with the equation:

$\displaystyle m=\frac{y_2-y_1}{x_2-x_1}$

Let's select two clear points from the graph: (0,100) (200,900)

Compute the slope:

$\displaystyle m=\frac{900-100}{200-0}=\frac{800}{200}=4$

The equation of the line is now:

y = 4x + b

To determine the value of b, we use any point from the graph: (0,100)

100 = 4(0) + b

Thus, b = 100

The full equation is:

y = 4x + 100