Question

which equation is the best fit for the data in the graph?
a y = 8x - 75
b y = 75x - 8
c y = -8x + 75
d y = -75x + 8

Explanation:

Step1: Analyze the trend of the data

The data in the scatter - plot shows a positive correlation. As the number of weeks (x) increases, the dollars in the piggy bank (y) increase.

Step2: Analyze the slope of the linear equations

For a linear equation \(y = mx + b\), if \(m>0\), the line has a positive slope (increasing trend), if \(m < 0\), the line has a negative slope (decreasing trend).

• In option A: \(y=8x - 75\), \(m = 8>0\) (positive slope)
• In option B: \(y = 75x-8\), \(m = 75\). This slope is too steep compared to the general trend of the scatter - plot.
• In option C: \(y=-8x + 75\), \(m=-8<0\) (negative slope)
• In option D: \(y=-75x + 8\), \(m=-75<0\) (negative slope)

Answer:

A. \(y = 8x-75\)