TSW calculate slope given two points

TSW calculate slope for parallel/perpendicular linesTSW write linear equations given slope and y-interceptTSW write linear equations given two pointsTSW rewrite linear equations in slope-intercept formTSW rewrite linear equations in Standard FormTSW write linear equations for horizontal/vertical lines

Review of Equations:

Formula for Slope m y2 y1

x2 x1

Ax By C

y mx b

y y1 m x x1

Standard Form

Slope-intercept Form

Point-Slope Form

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

m 6 4

1 3

2

4

1

2

Change into standard form.

y 3

4x 2

4 y 4 3

4x 4 2

3x 4y 8

3x 4y 8

Change into slope-

intercept form and identify m and b.3x 5y 15

5y 3x 15 5y

5

3x

5

15

53

35

y x 35

5m and b

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

Find the slope: m 7 5

1 2

2

3

Use point-slope form:

y 5 2

3x 2

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 = -2Write 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 = 1Write an equation of a line that passes through (3, 5) and (3, -2).

x = 3

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.

Write the equation of a line parallel to 2x – 4y = 8 and containing (-1, 4):

Write the equation of a line parallel to 2x – 4y = 8 and containing (-1, 4),

continued:

y y1 m x x1

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.

Write the equation of a line perpendicular to y = -2x + 3 and containing (3, 7):

Original Slope= -2

y y1 m x x1

y y1 m x x1

Write the equation of a line perpendicular to 3x – 4y = 8 and containing (-1, 4):

-4y = -3x + 83

24

y x

oComplete worksheet .oThis worksheet is considered your final study guide for the entire Chapter 5.