Graph Linearization

• Graph Linearization trains the skill of turning a curved graph into a straight line, so the slope and intercept reveal a physical quantity.

• Choose an equation from AP Physics 1 or AP Physics 2, decide what to put on each axis, and apply transforms such as squaring, square roots, or 1/x until the data falls on a line.

• When the graph is straight, the tool converts the slope (and the y-intercept, when it carries meaning) into the physics: for example, a pendulum's slope becomes a value of g.

• Explore mode shows every equation with its variables labeled, plus step-by-step hints. Practice mode hides the variables and builds a streak.

• Note for teachers: This mirrors what students do with lab data and on AP free-response questions: identify the relationship, pick the axes that make it linear, and connect the slope to the physics.

Usage Steps

Course

• Choose Both, AP Physics 1, or AP Physics 2. The course filter applies to Explore and Practice.

• Note for teachers: AP Physics 1 classes can stay on the AP Physics 1 filter so students only see equations they have studied.

Equations

• Pick an equation from the list, or narrow it with the search box or the topic buttons (Kinematics, Forces, Thermodynamics, and so on).

• A green check marks an equation you solved on your own. A book icon marks one you solved with the Walkthrough.

• The counter at the top and the numbers on each topic button track your progress.

Graph Setup

• Choose the x-axis variable first, then the y-axis variable. The y-axis menu only lists variables that pair with your x-axis choice.

• A greyed-out menu means there is only one choice for that equation.

• Changing either variable starts a fresh graph and clears your transforms.

• Mastery tip: Before touching the transforms, predict the shape of the raw graph from the equation. Will it curve up, curve down, or already be straight?

Data and Axis Quantities

• Some setups ask you to combine measured variables on an axis, like PV or Δx/t. These setups show an x-axis quantity and y-axis quantity menu instead of the variable menus.

• The ideal gas law has a Data switch: "One of P, V, T held constant" gives the usual graphs, and "P, V and T all change" gives a data set where you must combine quantities.

• The quantity menus include some combinations that will not work. Choosing the right one is part of the problem.

• Mastery tip: Rearrange the equation so the quantity you want to find sits where the slope goes. For PV = nRT, writing PV = n(RT) shows that PV vs RT has slope n.

Transforms

• Each axis has its own transform menu: raw, x², x³, √x, 1/x, 1/x², 1/√x, and ln. Angle variables also offer sin.

• The graph and data table update as soon as you change a transform.

• A dashed best-fit line appears when the graph is straight and matches the physics.

• If a transform can't be applied to some data points (the log of a negative number, or 1 divided by zero), those points disappear from the graph and a note explains why.

• Mastery tip: Change one axis at a time and watch how the curve bends. It teaches you which transform straightens which shape.

Check

• Press Check when you think the graph is linear.

• A correct answer shows the slope, what the slope represents, and the physical quantity it gives. When the y-intercept has meaning (like v₀), it is converted too.

• Correct rearrangements count. For example, √Δx vs t works as well as Δx vs t², and the tool shows how its slope connects to the usual graph.

• Some graphs come out straight without revealing anything, such as squaring both axes or taking ln of both. Check explains why those don't count.

• Reset sets both transforms back to raw.

Walkthrough

• Walkthrough reveals hints one at a time, from noticing the shape of the graph to reading the slope.

• An equation solved after opening the Walkthrough gets a book icon in the equation list instead of a green check.

• Mastery tip: Open only one hint, then try again on your own.

Data Table

• The table lists the raw data and the values on each axis after your transforms.

• For combined setups, it shows each measured variable (for example T, V and P) followed by the values you chose to graph.

• Note for teachers: The table is a good model for how students should set up their own lab data tables, with one column per transformed quantity.

Practice Mode

• Switch to Practice and press Start practice. Each problem is an unknown equation: the axes are labeled A and B and the variable names are hidden.

• Choose All or Needs transform to include or skip graphs that are already straight.

• Find the transforms, press Check, and build a streak. A correct answer reveals the equation and what the slope means.

• Skip moves to a new problem and resets your streak. The session tally counts first-try solves separately from solves after a wrong Check.

• Setups that combine quantities (PV vs RT, Δx/t vs t, Δθ/t vs t) appear in Explore only.

• Mastery tip: In Practice, name the relationship before choosing transforms: inverse, inverse square, square root, or exponential.