Question

each day for two weeks, howard recorded values for the following two variables. - the number of students ahead of him in the lunch line when he got in line, ( m ), - the number of minutes elapsed between when he got in line and when he sat down to eat he then plotted his data on a scatter plot, with the horizontal axis representing ( s ) and the vertical axis representing ( m ), and drew a line of best fit. the equation of the line was ( m = -\frac{1}{4}s + 1 ) according to the equation of the line, if there are 52 students ahead of howard when he gets in the lunch line, how many minutes should he expect it to take before he sits down to eat? (\boxed{\text{minutes}})

Explanation:

Step1: Identify variables

Here, horizontal axis is \( s \) (students ahead) and vertical axis is \( m \) (minutes elapsed). The equation is \( m = \frac{1}{4}s + 1 \). We need to find \( m \) when \( s = 52 \).

Step2: Substitute \( s = 52 \) into the equation

Substitute \( s = 52 \) into \( m = \frac{1}{4}s + 1 \). So, \( m=\frac{1}{4}\times52 + 1 \).

Step3: Calculate the value

First, calculate \( \frac{1}{4}\times52 = 13 \). Then, \( 13 + 1 = 14 \).

Answer:

14