Transcript Chapter 1 Linear Functions - Shelton State Community College

Chapter 1
Linear Functions
Section 1.1
Slopes and Equations of Lines
The Coordinate Plane
Slope of a Line
Finding the Intercepts of an Equation
 To find the y-intercept of an equation of a
line, substitute zero for x and solve for y.
 To find the x-intercept of an equation of a
line, substitute zero for y and solve for x.
 Example: Find the x-and y-intercept of the
line represented by 3x - 4y = -12.
Slope of a Line
Example 1
 Find the slope of the line that passes
through
a.) (-4, -3) and (2, -7).
b.) (5, 8) and (-1, 8)
c.) (12, -2) and (12, -9)
Special Cases of Slope
 The slope of a horizontal line is zero.
 The slope of a vertical line is undefined.
Equations of a Line
 An equation in two first-degree variables has a
line as its graph and is called a linear equation.
 The standard form of the equation of a line is
Ax + By = C.
Slope-Intercept Form
Example 2
 Find the equation of the line having a
slope of -3/5 and a y-intercept of (0, -1).
Point-Slope Form
Example 3
 Find the equation of the line that passes
through (-3, 1) and (-2, -4). Write the
answer in slope-intercept form.
Equations of Lines
Perpendicular and Parallel Lines
Example 4
 Write the equation of the line that passes
through (-1, -4) and is parallel to 4x + 2y = 10.
 Write the equation of the line that passes
through (7, 3) and is perpendicular to y = 3x -1.
Example 5
 Write the equation of the line that is parallel to
y = 10 and passes through (5, 8).
 Write the equation of the line that is
perpendicular to x = -3 and passes through
(-4, -1).