Question

warm-up
use the drawing tools to form the correct answer on the graph.
anna is saving to buy some souvenirs on a family vacation. she has already saved $125, and she saves another $2 from her allowance every day.
formulate and then graph the equation that models the total amount anna saves, y, in terms of the number of days she adds to her savings, x.

Explanation:

Step1: Identify the slope and y - intercept

The total amount saved \(y\) is a linear function of the number of days \(x\). The general form of a linear equation is \(y = mx + b\), where \(m\) is the slope (rate of change) and \(b\) is the y - intercept (initial value).
Anna already has $125 saved, so the y - intercept LXI0. She saves $2 per day, so the slope \(m=2\).

Step2: Formulate the equation

Substitute \(m = 2\) and \(b = 125\) into the linear equation \(y=mx + b\). We get the equation \(y=2x + 125\).

Step3: Find two points to graph the line

• When \(x = 0\) (no days of saving additional money), \(y=2(0)+125=125\). So the point is \((0,125)\).
• When \(x = 25\), \(y=2(25)+125=50 + 125=175\). So the point is \((25,175)\). We can plot these two points \((0,125)\) and \((25,175)\) (or other points calculated from the equation) and draw a line through them.

Answer:

The equation is \(y = 2x+125\). To graph it, plot the point \((0,125)\) (since when \(x = 0\), \(y = 125\)) and use the slope \(2\) (for every 1 unit increase in \(x\), \(y\) increases by 2 units) to find other points (e.g., \((1,127)\), \((2,129)\), etc.) and draw a line through them.