Cheat Sheet
5 sections
•
25 key points
1
Forms of Linear Equations
Slope-Intercept Form: y = mx + b (m = slope, b = y-intercept)
Point-Slope Form: y - y₁ = m(x - x₁) (m = slope, (x₁, y₁) = a point)
Standard Form: Ax + By = C (A, B, C are constants)
Horizontal Line: y = k (slope = 0)
Vertical Line: x = k (undefined slope)
2
Calculating Slope (m)
From two points (x₁, y₁) and (x₂, y₂): m = (y₂ - y₁) / (x₂ - x₁)
Positive slope: line rises from left to right.
Negative slope: line falls from left to right.
Zero slope: horizontal line.
Undefined slope: vertical line.
3
Graphing Linear Equations
Plot the y-intercept (b) first.
Use the slope (m = rise/run) to find a second point.
Draw a straight line connecting the points.
For standard form, find x and y intercepts.
Can also create a table of values.
4
Systems of Linear Equations
Substitution Method: Solve one equation for a variable, substitute into the other.
Elimination Method: Multiply equations to make coefficients opposite, then add.
Graphing Method: Find the intersection point of the lines.
One solution: Intersecting lines.
No solution: Parallel lines.
5
Linear Inequalities
Solve like equations, but reverse inequality sign if multiplying/dividing by a negative.
Graph boundary line: solid for ≤, ≥; dashed for <, >.
Shade the region: test a point (0,0) if not on line to determine shading.
y > mx + b: shade above the line.
y < mx + b: shade below the line.
Sample Flashcards
Card 1 of 6
Question
Formula for slope-intercept form
Answer
y = mx + b
Click the card to flip
Quick Quiz
1. What is the slope of the line y = 3x - 5?
2. A line passes through (1, 2) and (3, 8). What is its slope?
3. Which of these points is a solution to the inequality y > 2x + 1?
4. Which method involves adding or subtracting equations to eliminate a variable?
5. What is the y-intercept of the equation 2x + 3y = 6?
Frequently Asked Questions
What is the slope-intercept form?
The slope-intercept form is y = mx + b, where 'm' is the slope and 'b' is the y-intercept.
How do you graph a linear inequality?
Graph the boundary line (solid for ≤ or ≥, dashed for < or >) and then shade the region that satisfies the inequality.
What is a system of linear equations?
A system of linear equations consists of two or more linear equations with the same variables. The solution is the point(s) that satisfy all equations.
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