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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