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Math Topics
High School Algebra 2
Slope, Rates of Change, and Linear Functions
1
The Slope of a Line
A patient tells her doctor that she is experiencing hypoglycemia during her workouts at the gym. Her doctor gives her a blood testing kit and has her repeat her workout, monitoring her blood sugar level every \(5\) minutes, and noting any symptoms she is experiencing. The results are shown in Figure 7.
After looking at the graph, her doctor said, “The first time you felt poorly, you were sensing the rate of change in your blood sugar level, but you were probably not experiencing hypoglycemia until your sixth reading.â€
a. Is her first experience of feeling poorly because of the slope of a line, or a point on the graph?
b. Is she feeling poorly at her sixth reading because of the slope of a line, or a point on the graph?
Mini Lecture
Find the slope through the given points.
\((3,\, 1)\) and \((5,\, 4)\)
\((-3,\, 2)\) and \((3,\, -2)\)
Find the slope of the line with an \(x\)-intercept of \(4\) and a \(y\)-intercept of \(2\).
Find \(a\) if the line through \((5,\, a)\) and \((4,\, 2)\) has a slope of \(3\).
Find \(y\) if the line through \((2,\, y^2)\) and \((1,\, y)\) is \(\bot\) to a line with slope \(-\dfrac{1}{6}\).
2
Linear Functions and Equations of Lines
It cost a bicycle company \(\$9000\) to make \(50\) touring bikes in its first month of operation and \(\$15,000\) to make \(125\) bikes during its second month.
a. Find a linear equation for the company’s monthly production cost \(C\) in terms of the number of bikes made, \(x\).
b. State the slope and vertical intercept of your line, including units. What do they tell you about the problem?
3
Linear Regression
4
Variation
The distance a skydiver falls is directly proportional to the square of the time he has been falling. If the skydiver falls \(64\) feet in the first \(2\) seconds.
How far will he have fallen after \(3.5\) seconds?
Graph the relationship between distance and time.
How long will it take him to fall \(256\) feet?
In electricity, the resistance of a cable is directly proportional to its length and inversely proportional to the square of the diameter. If a \(100\) foot cable \(0.5\) inch in diameter has a resistance of \(0.2\) ohm, what will the resistance of a cable made from the same material if it is \(200\) feet long with a diameter of \(0.25\) inch?
Mini Lecture
\(y\) varies directly as \(x\). If \(y=39\) when \(x=3\), find \(y\) when \(x\) is \(10\).
\(y\) varies inversely as the square of \(x\). If \(y=4\) when \(x=3\), find \(y\) when \(x\) is \(2\).
The power \(P\) is an electric circuit varies directly with the square of the current \(I\). If \(P=30\) when \(I=2\), find \(P\) when \(I=7\).
