Algebra: Slope and Graphing Cheat Sheet

Given the equation ( y = 2x - 5), what is the slope and y-intercept?

What is the slope of the line that passes through the points (3, 5) and (7, 13)?

If the equation of a line is y = 4x, what type of relationship exists between the input and output?

The equation ( 2x + y = 4 ) is in standard form. Which form would this equation be in after being converted into slope-intercept form?

Which of the following is NOT a valid way to represent the slope of a line?

Slope-Intercept Form

Graphing with y-intercept

Slope and Graphing "Cheat Sheet"

Slope (m): Constant rate of change, calculated using ordered pairs (x₁, y₁) and (x₂, y₂). Formula: (y₂ - y₁) / (x₂ - x₁). Used with graphs to find the "rise over run."

Slope-Intercept Form (not proportional)

Formula: y = mx + b, where:
- 'm' is the slope
- 'b' is the y-intercept (the point where the line crosses the y-axis)

Direct Variation (proportional)

Formula: y = kx, where 'k' is the constant of variation (same as the unit rate).

Equation Examples

Examples of equations:
- y = 3x + 6
- y = x - 6
- -4x + y = -3

Graph Examples

Graphing:
- Graphs illustrate the relationship between the variables (input and output) based on a given equation.
- Examples include graphs with and without y-intercepts (points where the graph crosses the y-axis) are shown.

Table Examples

Tables:
- Tables provide numerical values for the variables (x and y).
- Examples illustrate how the proportional and non-proportional relationships can be shown in a table.

Types of Slope

Positive Slope: The line slants upward from left to right.
Negative Slope: The line slants downward from left to right.
Zero Slope: The line is horizontal.
Undefined Slope: The line is vertical.

Master the concepts of slope and graphing with this cheat sheet. Learn about the slope-intercept form, direct variation, and explore equation examples along with graph and table interpretations. Perfect for quick revisions and understanding relationships between variables.