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.

Test your understanding of parallel, perpendicular, and neither types of lines in algebra. This quiz covers how to graph lines, find equations using points, and calculate slopes. Perfect for reinforcing key concepts in your Algebra curriculum.