Chapter 1, "Points and Lines"

Equation of a Line

The graph of an equation of the form Ax + By = C, where A and B are not both 0, is a straight line.

Slope

For any line in standard form, Ax + By = C, the slope m = –A/B.

Parallel Lines

If two lines are parallel, their slopes must be equal.

Perpendicular Lines

If two lines are perpendicular,

Equation of a Line

Slope-intercept form: y = mx + b

Point-slope form: (y – y₁) = m(x – x₁)

where (x₁,y₁) is a point on the line.

System of Linear Equations

A system of two linear equations in the same plane has

• Exactly one solution if the two graphs have different slopes.

• An infinite set of solutions if both graphs have the same slope and y-intercept.

• No solution if the graphs have the same slope but different y-intercepts.