Question

janelyss math teacher plots student grades on their weekly quizzes against the number of hours they say they study on the pair of coordinate axes and then draws the line of best fit. based on the line of best fit, how much time should someone study to expect a quiz score of 97? answer attempt 1 out of 2 hours per week submit answer

Explanation:

Step1: Find the slope formula

The slope formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Using the points \((3.5,85)\) and \((4,88)\), we have \(m=\frac{88 - 85}{4 - 3.5}=\frac{3}{0.5}=6\).

Step2: Find the y - intercept formula

The equation of a line is \(y=mx + b\). Using the point \((3.5,85)\) and \(m = 6\), we substitute into the equation: \(85=6\times3.5 + b\). Then \(85 = 21+b\), and \(b=85 - 21=64\). So the equation of the line of best - fit is \(y = 6x+64\).

Step3: Solve for x when y = 97

Substitute \(y = 97\) into \(y = 6x+64\). We get \(97=6x + 64\). Subtract 64 from both sides: \(97-64=6x\), so \(33 = 6x\). Then \(x=\frac{33}{6}=5.5\approx5\) (rounding to the nearest whole number as per the context of the problem).

Answer:

5