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Linear Functions

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Linear Functions

Formula for Slope

Standard Form

*where A>0 and A, B, C are integers

Slope-intercept Form

Point-Slope Form

Find the slope of a line through points (3, 4) and (-1, 6).

Change into standard form.

Change into slope-intercept form and identify the slope and y-intercept.

Write an equation for the line that passes through (-2, 5) and (1, 7):

Find the slope:

Use point-slope form:

x-intercepts and y-intercepts

The intercept is the point(s) where the graph crosses the axis.

To find an intercept, set the other variable equal to zero.

Horizontal Lines

- Slope is zero.
- Equation form is y = #.

- Write an equation of a line and graph it with zero slope and y-intercept of -2.
- y = -2
- Write an equation of a line and graph it that passes through (2, 4) and (-3, 4).
- y = 4

Vertical Lines

- Slope is undefined.
- Equation form is x = #.

- Write an equation of a line and graph it with undefined slope and passes through (1, 0).
- x = 1
- Write an equation of a line that passes through (3, 5) and (3, -2).
- x = 3

- Graphing Lines
*You need at least 2 points to

graph a line.

Using x and y intercepts:

- Find the x and y intercepts
- Plot the points
- Draw your line

Graph using x and y intercepts

2x – 3y = -12

x-intercept

2x = -12

x = -6

(-6, 0)

y-intercept

-3y = -12

y = 4

(0, 4)

Graph using x and y intercepts

6x + 9y = 18

x-intercept

6x = 18

x = 3

(3, 0)

y-intercept

9y = 18

y = 2

(0, 2)

- Graphing Lines
Using slope-intercept form y = mx + b:

- Change the equation to y = mx + b.
- Plot the y-intercept.
- Use the numerator of the slope to count the
- corresponding number of spaces up/down.
- Use the denominator of the slope to count the corresponding number of spaces left/right.
- Draw your line.

Slope

m = -4 = -4

1

y-intercept

(0, 1)

Graph using slope-intercept form y = -4x + 1:

Slope

m = 3

4

y-intercept

(0, -2)

Graph using slope-intercept form

3x - 4y = 8

y = 3x - 2

4

- Parallel Lines
- **Parallel lines have the same slopes.
- Find the slope of the original line.
- Use that slope to graph your new line and to write the equation of your new line.

Graph a line parallel to the given line and through point (0, -1):

Slope = 3

5

Write the equation of a line parallel to

2x – 4y = 8 and containing (-1, 4):

– 4y = - 2x + 8

y = 1x - 2

2

Slope =1

2

y - 4 = 1(x + 1)

2

- Perpendicular Lines
- **Perpendicular lines have the
- opposite reciprocal slopes.
- Find the slope of the original line.
- Change the sign and invert the
- numerator and denominator
- of the slope.
- Use that slope to graph your new
- line and to write the equation
- of your new line.

Graph a line perpendicular to the given line and through point (1, 0):

Slope =-3

4

Perpendicular

Slope=4

3

Write the equation of a line perpendicular to

y = -2x + 3and containing (3, 7):

Original Slope= -2

Perpendicular

Slope =1

2

y - 7 = 1(x - 3)

2

Write the equation of a line perpendicular to

3x – 4y = 8 and containing (-1, 4):

-4y = -3x + 8

y - 4 = -4(x + 1)

3

Slope= 3

4

Perpendicular

Slope = -4

3