Question

1. what is the equation of the line that goes through the points (-2, 4) and (-1, 7)?

hint: use the formula sheet to determine the formula(s) needed to solve the problem.
a ( y = \frac{1}{3}x - 10 )
b ( y = \frac{1}{3}x + 10 )
c ( y = 3x + 10 )
d ( y = 3x - 10 )

1. sugar level in patient’s bloodstream

a doctor measured the blood sugar levels of one of her patients shortly after giving the patient a candy bar to eat. the graph below shows the patient’s blood sugar level (y) x hours after she ate the candy bar.
how long after eating the candy bar was the patient’s blood sugar level the highest?
(a) 20 minutes
(b) 30 minutes
(c) 40 minutes
(d) 1 hour

Explanation:

Question 18

Step1: Calculate the slope

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(-2,4)\) and \((x_2,y_2)=(-1,7)\). Then \(m=\frac{7 - 4}{-1-(-2)}=\frac{3}{1}=3\).

Step2: Use the point - slope form

The point - slope form is \(y - y_1=m(x - x_1)\). Using \(m = 3\) and the point \((x_1,y_1)=(-2,4)\), we have \(y-4=3(x + 2)\).

Step3: Simplify the equation

Expand \(y-4=3x+6\). Then \(y=3x + 10\).

The \(x\) - axis represents the time since the sugar was ingested (in hours). The \(y\) - axis represents the sugar level. The highest \(y\) - value (sugar level) occurs at \(x=\frac{1}{3}\) hours. Since \(1\) hour \( = 60\) minutes, \(\frac{1}{3}\times60 = 20\) minutes.

Answer:

C. \(y = 3x+10\)

Question 19