Question

study to expect a quiz score of 83? answer attempt 2 out of 2 hours per week

Explanation:

Step1: Find the slope of the line

We use two points on the line, say $(3.5,77)$ and $(4,80)$. The slope $m$ formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. So $m=\frac{80 - 77}{4 - 3.5}=\frac{3}{0.5}=6$.

Step2: Find the y - intercept

Using the point - slope form $y - y_1=m(x - x_1)$ with the point $(3.5,77)$ and $m = 6$, we have $y-77 = 6(x - 3.5)$. Expanding gives $y-77=6x-21$, so $y = 6x + 56$.

Step3: Solve for x when y = 83

Set $y = 83$ in the equation $y = 6x+56$. Then $83=6x + 56$. Subtract 56 from both sides: $83 - 56=6x$, so $27 = 6x$. Divide both sides by 6: $x=\frac{27}{6}=4.5$.

Answer:

4.5