Algebra II Unit 1 Test Flashcards

Slope Concepts

• Slope formula is defined as ((y_2 - y_1) / (x_2 - x_1)).
• A rising slope has a positive value indicating the line slopes upwards from left to right.
• A falling slope has a negative value indicating the line slopes downwards from left to right.
• A vertical slope occurs when the denominator in the slope formula equals zero, representing a line that goes straight up and down.
• A horizontal slope has a value of zero, indicating there is no change in the y-coordinate as x varies.

Line Relationships

• Two lines are parallel if they have identical slopes.
• Two lines are perpendicular if their slopes are opposite reciprocals, meaning one slope could be expressed as (-1/m) if the other slope is (m).

Finding Missing Coordinates

• To find a missing coordinate:
  • Insert known values into the slope formula.
  • Solve for the side of the fraction containing the unknown.
  • Multiply the known number by the slope.
  • Set the product equal to the other half of the fraction and solve for the unknown.

Forms of Linear Equations

• Standard form of a linear equation is represented as (Ax + By = C).
• To find (x) from a standard form equation, substitute (0) for (y) and solve.
• To find (y) from a standard form equation, substitute (0) for (x) and solve.

Equation Formats

• Slope-intercept form is expressed as (y = mx + b), where (m) represents the slope and (b) is the y-intercept.
• Point-slope form is represented as (y - y_1 = m(x - x_1)).

Parallel and Perpendicular Lines

• To establish a line parallel to a given slope, use the given slope and any point in point-slope form.
• To establish a line perpendicular to a given slope, use the opposite reciprocal of the slope from the given line and apply any point in point-slope form.

Graphing Inequalities

• When graphing inequalities:
  • Use a solid line if the inequality sign includes an equal to (≤ or ≥).
  • Use a dotted line if the inequality is strict (< or >).
• Steps for graphing an inequality:
  • Graph the corresponding line.
  • Choose a test point to substitute into the inequality.
  • Solve the inequality with the chosen coordinates.
  • If the result is true, shade the region of the graph corresponding to the test point.

Modeling Linear Functions

• Model linear functions by identifying time and numeric conditions relevant to the scenario.
• Represent these conditions as coordinates.
• Use the coordinates to formulate the problem into slope-intercept form and solve accordingly.