Question

after reading equation of the line from the graphing utility, heather wrote in her notebook that the line of best fit is represented by the equation y = 0.77x + 1.34. heather likely an error when writing the equation of the line in her notebook because the slope and the y - intercept of the equation she recorded

Explanation:

Step1: Analyze the general form of a line

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

Step2: Estimate slope visually

By looking at the scatter - plot and the line of best fit, we can see that the line rises more than 1 unit for every 1 unit it runs to the right. So the slope $m> 1$. But Heather's equation has a slope $m = 0.77<1$.

Step3: Estimate y - intercept visually

The line of best fit intersects the y - axis at a value close to 1. But Heather's equation has a y - intercept $b = 1.34$ which is a bit off from the visual estimate.

Answer:

made; do not match the visual estimate of the line of best fit from the graph.