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