Trigonometry/ Pre-Calculus Chapter P: Prerequisites Section P.3: Lines in the Plane

Lines in the Plane Slope = Delta,, means “change in” Given two points in the plane:

Point Slope Form of a Linear Equation Given two points in the plane: Point-slope form: Find Slope & Cross-multiply Now, switch sides

Slope-Intercept Form of a Linear Equation Slope-intercept form: m is the slope of the given line b is the y -intercept of the given line  the point (0, b) is on the graph

General Form of a Linear Equation General Form : Ax + By + C = 0 Where A, B, and C are integers & both A and B cannot be 0

Equations of special lines Vertical lines intersect the x -axis, therefore the equation of a vertical line is x = a Where a is the x -intercept x = 3 intersects the x -axis at 3 Slope is undefined Horizontal lines intersect the y -axis, therefore the equation of a horizontal line is y = b Where b is the y -intercept y = 3 intersects the y -axis at 3 Slope is 0

Parallel and Perpendicular Parallel lines never intersect, therefore they have the SAME SLOPE Perpendicular lines intersect at right angles, therefore they have OPPOSITE INVERSE SLOPES

Clearing Fractions To clear the fractions, multiply EVERY term by the common denominator Example: C.D.= General Form

Example Ex. 1 Find the equation of the line that passes through the point ( 2, -1 ) and is perpendicular to the line First, find slope of given line by setting it up in slope-intercept form Find the opposite reciprocal slope Use this slope and the given point to find new equation

Example continued

Example Continued If the slope of the given line is, then the slope of the line that is perpendicular to it is: Now, use this slope and the given point given to find the equation

Example Continued Use point-slope form