Question

what is the equation of the line that best fits the given data? a. y = 2x + 1 b. y = x c. y = x + 1 d. y = -x

Explanation:

Step1: Recall slope - intercept form

The equation of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept.

Step2: Analyze the y - intercept

The line of best - fit should cross the y - axis around $y = 1$. This eliminates option b ($y=x$ with $b = 0$) and option d ($y=-x$ with $b = 0$).

Step3: Analyze the slope

The points seem to have a positive slope. The slope of the line passing through the points appears to be close to 1 rather than 2. For option a ($y = 2x+1$), the slope $m = 2$ which is too steep for the given data points. For option c ($y=x + 1$), the slope $m = 1$ and the y - intercept $b = 1$, which seems to fit the data well.

Answer:

C. $y=x + 1$