L4. Test Slope of a Line, Parallel and Perpendicular Lines and Equations, Writing Equations in Point-Slope and Slope-Intercept Form

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What is the slope of a line parallel to the line 3x + 8y = 17.

-3/8

4/5

-What is the slope of a line perpendicular to the line 4x - 5y = -18

negative slope

A line that moves downward from left to right has a negative slope.

positive slope

A line that moves upward from left to right has a positive slope.

rise/run

A method to determine slope of a line

linear equation

An equation whose graph forms a straight line; often written in the form, y = mx + b.

y=mx + b

Equation of a straight line

y + 1= 1/2(x-4)

Find the point slope equation:

y - 1 = 2(x - 1)

Find the point slope equation:

y - 1 = 3/4(x + 2)

Find the point slope equation:

y - 3 = -2/3(x + 4)

Find the point slope equation: (-4, 3) m = -2/3

y - 10 = 6/7(x + 9)

Find the point slope equation: (-9, 10) m = 6/7

y - 3 = 3/4(x - 2)

Find the point slope equation: (2, 3) m = 3/4

3/2

Find the slope given the following points: (1,1), (3,4)

7/ 5

Find the slope given the following points: (5,7), (10,14)

-1

Find the slope.

-2

Find the slope.

-5/4

Find the slope.

0

Find the slope.

1/2

Find the slope.

4

Find the slope.

undefined - no slope

Find the slope.

-1/6

Find the slope..

-3/4

Find the slope...

-5/4

Find the slope...

7/8

Find the slope...

(-4,2)

The point (coordinate) for this equation: y - 2 = 4(x + 4)

(-3,4)

The point (coordinate) for this equation: y - 4 = 2/3(x + 3)

(3,4)

The point (coordinate) for this equation: y - 4 = 2/3(x - 3)

slope (unit rate/rate of change)

The ratio of the vertical change to the horizontal change of any two points on a line, and is constant.

y = mx + b

This is slope intercept form (without numbers)

y - y1 = m(x - x1)

This is the point slope equation (without numbers)

Steepness of a line

What does the term "Slope" refer to?

y = 7x -9

Write an equation of a line that is parallel to the lines y = 7x + 2 that passes through (1,-2).

y = -1/7x - 13/7

Write an equation of a line that is perpendicular to the line y = 7x + 2 that passes through (1,-2).= -1/7x - 13/7

y-5 = -(x-3)

Write the equation in point-slope form of m = -1 and (3, 5)

y + 3 = -1/4(x - 4)

Write the equation in point-slope form of m= -1/4 and (4, -3)

y - 0 = 2(x + 1)

Write the equation in point-slope form of m= 2 and (-1, 0)

y + 6 = 2/5(x + 5)

Write the equation in point-slope form of m= 2/5 and (-5, -6)

y + 6 = 4 (x + 1)

Write the equation in point-slope form of m= 4 and (-1, -6)

y + 3 = 5(x + 2)

Write the equation in point-slope form of m= 5 and (-2, -3)

y = -2x + 13

Write the equation in slope-intercept form of m= -2 and (5, 3)

y = 1/2x - 4

Write the equation in slope-intercept form of m= 1/2 and (2, -3)

y = 1/2x + 5

Write the equation in slope-intercept form of m= 1/2 and (2, 6)

y = 3x + 3

Write the equation in slope-intercept form of m= 3 and (1, 6)

y = 4x - 11

Write the equation in slope-intercept form of m= 4 and (2, -3)

y = 5x + 7

Write the equation in slope-intercept form of m= 5 and (-1, 2)

y = -x

Write the equation in slope-intercept form of the line passing through the points (-1, 1) and (1, -1)

y = -4x -14

Write the equation in slope-intercept form of the line passing through the points (-6, 10) and (-3, -2)

y = ½x + 3

Write the equation in slope-intercept form of the line passing through the points (0, 3) and (2, 4)

y = 7x - 3

Write the equation in slope-intercept form of the line passing through the points (1, 4) and (3, 18)

y = -3x - 9

Write the equation in slope-intercept form of the line passing through the points (1, 6) and (2, 3)

y = 3x - 8

Write the equation in slope-intercept form of the line passing through the points (5, 7) and (3, 1)

y = ½x + 3

Write the equation in slope-intercept form of the line passing through the points (6, 6) and (-2, 2)

y = 10

Write the equation in slope-intercept form of the line passing through the points (7, 7) and (-3, 7)

y = 4x - 12

Write the equation of a line that passes through (2,-4) and is parallel to y = 4x - 6.

y = 5x +13

Write the equation of a line that passes through (4,7) and is parallel to y = 5x +3

y = 1/3x + 6

Write the equation of a line that passes through (-6,4) and is perpendicular to y = -3x +5.

y = 5/8 x + 33

Write the equation of a line that passes through the points (-24, 18) and (0, 33)

y = 5x - 22

Write the equation of a line that that passes through (3, -7) and is perpendicular to the line y = -1/5 x + 1

Parallel lines have slopes that are

equal

zero slope

horizontal 0/#

Perpendicular lines have slopes that are

negative reciprocals

undefined slope

vertical line #/0

Write the equation of a line that is parallel to the line x = 5.

x = a, where a is any number except 5

Write an equation of a line that is perpendicular to the line x = 5.

y = b, where b is any number.

slope-intercept form

y=mx+b

rate of change (slope)

Show the relationship between two changing quantities in a function as the ratio of the change in the dependent variable to the change in the independent variable.

(-7,-5)

The point (coordinate) for this equation: y + 5 = 3(x + 7 )


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