Algebra 1 Section 6 5 Linear Equations Standard

Algebra 1 Section 6. 5

Linear Equations Standard form: Ax + By = C Slope-intercept form: y = mx + b Point-slope form: y – y 1 = m(x – x 1)

Point-Slope Form of a Line The point-slope form provides an alternative method of determining the equation of a line from the slope (m) and any given point (x 1, y 1) on the line.

Example 1 Equation of the line passing through (-5, 2) and (3, -4): First, find the slope: y 2 – y 1 -4 - 2 -6 3 m= = = =x 2 – x 1 3 -(-5) 8 4

Example 1 y – y 1 = m(x – x 1) y -(-4) = -¾(x – 3) 3 9 y+4=x+ 4 4 3 7 y=x– 4 4

Example 1 3 7 y=x– 4 4 To standard form: 4 y = -3 x – 7 3 x + 4 y = -7

Definitions Parallel lines are lines in the same plane that have no points in common. Perpendicular lines meet at right angles (90°).

Parallel Lines The graphs of linear equations are parallel if they have the same slope but different yintercepts.

Example 2 3 x – y = 6 y = 3 x – 6 -9 x + 3 y = 12 y = 3 x + 4 m 1 = 3 y-int: (0, -6) m 2 = 3 y-int: (0, 4) The lines are parallel.

Example 3 Find the slope of 4 x + 3 y = 17. 4 m=3 The parallel line has the same slope, and goes through the point (-5, 9).

Example 3 y – y 1 = m(x – x 1) 4 y– 9=[x -(-5)] 3 4 20 y– 9=x– 3 3 4 7 y=x+ 3 3

Slopes Parallel lines have the same slope. Perpendicular lines have slopes that are negative reciprocals of each other.

Example 4 Number 8 5 9 Negative Reciprocal 5 8 1 9

Example 4 Number 13 7 a Negative Reciprocal 7 13 1 a

Example 5 The slope of y = -4 x + 9 is -4. Find the slope of a line 1 perpendicular to it: m = 4 The perpendicular line has a slope of ¼, and goes through the point (2, 7).

Example 6 2 x + 5 y = 9 4 x + y = 1 2 9 y = -4 x + 1 y=x+ 5 5 m 2 = -4 2 m 1 = 5 The lines are neither parallel nor perpendicular.

Homework: pp. 259 -261