MAC 1140 – Section 1.4 – Linear Functions
Review of Linear Function Vocabulary, Definitions and Formulas
Forms of a linear function:
Slope-intercept:y = mx + b where m = slope and b = y-intercept
Point-slope: y – y1 = m(x – x1)
Standard: Ax + By = C where A, B, and C are integers
When the directions are: Use the form:
Find the slope and y-interceptslope-intercept
Sketch the graphslope-intercept
Write the equation of the linepoint-slope
Solve a system of equationsStandard
Special Lines:
Vertical: x = #
Horizontal: y = #
Parallel: have the same slope
Perpendicular: slopes are opposite reciprocals (if one is m the other is –1/m)
Slope formula: m = =
Use these formulas and definitions to solve the following:
A. Sketch the graph of: 1. 2. 3.
1. y = 3x – 5
2. y =
3. 3x + 2y = 5
4. 5.
4. y = 7
5. x = 2
B. Find the slope of the line passing through the following pairs:
1. (4, 6) (2, -8)2. ( -8, -4), (-2, -5) 3. (3.41, -2.6) (5.87, -3.71) (May use calculator.)
C. Write the equation of the line………
In slope-intercept form:
1. Passing through (5,1) with a slope of 22. Passing through (4, 6) (2, -8)
In point-slope form:
3. Passing through (2,7) parallel to y = 4x – 24. Passing through (2, 7) parallel to 4x – 2y = 12
In standard form:
5. Passing through (2,7) perpendicular to 4x - 2y = 12
6. Passing through (2,7) perpendicular to 4x + 3y = 12
As Special Lines:
7. Passing through (2,7) parallel to y = 58. Passing through (2,7) perpendicular to y = 5
HOMEWORK: Page 48: Problems 1, 3, 5, 11-17odds, 27, 29, 37, 41, 57, 59, 63, 65, 67, 38, 46, 66
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