Master SAT function notation and behavior with this 10-question set, analyzing linear/quadratic function transformations.
Linear Equations Tips and Tricks
- A linear equation graphs as a straight line.
- Think of a linear equation in two parts:
a starting value and a constant rate of change. - Slope tells you how fast the line rises or falls.
- A positive slope means the line rises from left to right.
- A negative slope means the line falls from left to right.
- A zero slope means the line is horizontal, or flat.
- An undefined slope means the line is vertical.
- The y-intercept is the point where the line crosses the y-axis.
- In slope-intercept form (y = mx + b), the slope and starting value are easiest to identify.
- In standard form (Ax + By = C), it is often easier to find the intercepts.
- To find the slope from two points, compare the change in y-values to the change in x-values.
- Parallel lines have the same slope.
- Perpendicular lines have opposite reciprocal slopes.
- In word problems, the slope usually represents a rate, such as:
- cost per item
- miles per hour
- dollars earned per hour
- The y-intercept usually represents the starting amount, such as:
- a starting fee
- an initial value
- the amount when x = 0
- When graphing a line, start at the y-intercept, then use the slope as your movement pattern.
- Be careful not to confuse the x-intercept with the y-intercept.
- If an equation does not look linear at first, simplify it before deciding whether it is linear.
- On test questions, rate of change almost always points back to slope.
Quick Test-Day Reminder
Slope = rate of change.
Y-intercept = starting value.
Those two ideas unlock a huge number of linear-equation questions.