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Linear equations in two variables
I worked these out from the practice questions. Each code says where to start reading, where to stop, what you can skip, and why it is safe.
1. Put it in and test
- Start:
- The equation and the point or number given
- Stop:
- After the equation becomes true or false
- Skip:
- Rearranging the equation
- Why:
- Substituting beats algebra for easy questions (questions 1 and 2).
Used in questions 1, 2
2. Standard form slope is −A ÷ B
- Start:
- The coefficients in front of x and y
- Stop:
- When you have the slope
- Skip:
- Solving the equation for y
- Why:
- The shortcut −A ÷ B saves time (questions 3 and 6).
Used in questions 3, 6
3. Try each option as a point
- Start:
- The four answer choices
- Stop:
- When one choice fits both points
- Skip:
- The others once one fails
- Why:
- For writing equations, test both given points in the options (question 5).
Used in question 5
4. Intercepts: zero one letter
- Start:
- The equation
- Stop:
- When you find x and y with the other letter zero
- Skip:
- Graphing the whole line
- Why:
- Set x = 0 for y-intercept and y = 0 for x-intercept (questions 7 and 8).
Used in questions 7, 8
5. Area of the axis triangle is half product
- Start:
- The intercepts
- Stop:
- After ½ × x-intercept × y-intercept
- Skip:
- The slope
- Why:
- Always include the ½ (question 7).
Used in question 7
6. Word problem: use the given count
- Start:
- The line that gives how many of one item
- Stop:
- After you solve for the other count
- Skip:
- Rewriting the story
- Why:
- Put the given number into the total equation (question 4).
Used in question 4
7. Desmos: type the equation
- Start:
- The equation in the question
- Stop:
- When you read the point from the graph
- Skip:
- Handwork on long equations
- Why:
- Type the equation in Desmos and read the intercepts, or click the line to see them (questions 3, 7, 8).
Used in questions 3, 7, 8
8. Graph questions: read, then test the options
- Start:
- The labelled points and where the line meets the axes
- Stop:
- When one option works for every labelled point
- Skip:
- The decoration of the graph
- Why:
- Put each labelled point into the options. Only the true equation works for all of them (questions 9, 12, 14).
Used in questions 9, 12, 14
9. Parallel keeps the left side, perpendicular swaps it
- Start:
- The equation of the given line
- Stop:
- When you have the new left side
- Skip:
- Solving for the slope of every option
- Why:
- Parallel: same A and B, new constant. Perpendicular: swap A and B, change one sign, then use the point (questions 13 and 15).
Used in questions 13, 15
10. Intercept form x/a + y/b = 1
- Start:
- The sentence that says how the intercepts are related
- Stop:
- When you have an equation with only b
- Skip:
- Finding the slope
- Why:
- Writing x/a + y/b = 1 turns an intercept story into one equation (question 16).
Used in question 16