Algebra Class: Lines and Slopes

Parallel Lines

• Parallel lines have identical slopes, indicating that they run in the same direction.

Perpendicular Lines

• Perpendicular lines have slopes that are opposite reciprocals, meaning if one slope is m, the other is -1/m.

Neither Parallel Nor Perpendicular

• Lines that are neither parallel nor perpendicular have slopes that do not match and are not opposite reciprocals.

Graphing a Line from an Equation

• Begin by plotting the y-intercept on the graph.
• Utilize the slope to find additional points, or create a table to calculate x,y coordinates.

Finding the Equation from Two Points

• Calculate the slope (m) between the two points.
• Substitute the slope into the equation y = mx + b using one point to solve for the y-intercept.
• Alternatively, use the formula y1 - y2 = m(x1 - x2).

Finding the Equation from One Point and Slope

• Insert the known slope and coordinate of the point into the equation format y - y1 = m(x - x1).

Finding the Equation from a Parallel Line and Point

• Use the slope from the parallel line.
• Apply the given point to derive the new line's equation.

Finding the Equation from a Perpendicular Line and Point

• Obtain the opposite reciprocal of the slope from the given perpendicular line.
• Utilize the specified point to formulate the new line's equation.

Finding the Equation from a Graph

• Identify and mark at least two clear points on the graph.
• Determine the slope between those points.
• Choose one point to solve for the y-intercept.

Converting Between Forms

• In standard form, coefficients should be whole numbers and the x coefficient cannot be negative.
• To convert y = mx + b to Ax + By = C, rearrange and adjust constants accordingly.

Horizontal Lines

• A horizontal line has a slope of zero, indicating no vertical change as x changes.

Vertical Lines

• A vertical line has an undefined slope since it cannot be represented as a ratio of vertical change to horizontal change.