Perpendicular/Parallel
What determines that the slope of a line is parallel?
What determines that the slope of a line is perpendicular?
A parallel slope with result in the same number for both slopes.
A perpendicular slope will result in a negative reciprocal slope.
In the equation y= mx + b, what are m and b?
m = slope of the line
b = y-intercept (0,y)
With the equation y-y1 = m(x-x1) what can be determined when there are values.
The slope of the line as m, and a specific point that falls on the line.
What can be determined from using general form?
The x and y intercepts of a graph.
Anne Shirley is the primary character in what 1908 novel?
Anne of Green Gables
Line PQ passes through P( 7, 2) and Q( 2, 10).
Line RS passes through R( 3, 4) and S(5, 1).
Are these two lines parallel, perpendicular, or neither?
Line PQ = 8/5
Line RS = 5/8
The slopes are not the same, and they are not negative reciprocals, so the lines are neither.
The graph of a linear function has slope (-7/3) and y-intercept 5.
Write an equation for this function.
y = (-7/3)x + 5
This line has slope -3 and passes through P(-2, 5). What does this look like in slope-point form?
y - 5 = -3(x+2)
Change y = (-2/3)x + 4 into general form.
2x. + 3y -12 = 0
Name all 4 teenage mutant ninja turtles.
Raphael, Leonardo, Donatello, Michelangelo (Mikey)
Determine the slope of a line that is perpendicular to the line through E(2, 3) and F( 4, 1).
Slope of EF = 2/3
Slope of line perpendicular to EF = -3/2
Write an equation for the graph that passes through the point (0, 3) and has slope 7/16.
y = (7/16)x + 3
Describe the graph of the linear function with this
equation: y + 1 = (-1/2)(x - 4)
The slope of the graph is -1/2
A point along the line is (4, -1)
Is the equation -(1/5)x+ (2/5)y =10 in general form? If not, rearrange it.
0 = x - 2y + 50
In one of the most popular Dr. Seuss books, what won't Sam-I-Am eat?
Green eggs and ham
Line GH passes through G( 4, 2) and H(2, 1).
Line JK passes through J( 1, 7) and K(7, 3).
Line MN passes through M( 4, 5) and N(5, 1). Which lines are parallel?
GH and JK are equal slopes, the two lines are parallel. (-1/2)
MN is different from the slopes of GH and JK,MN is not parallel to those lines.
An equation of a line is y= (5/3)x +b. Determine
the value of b when the line passes through the
point F(4,-6).
b = (-38/3)
Write an equation for the line that passes through R(1, -1) and is perpendicular to the line y = (2/3)x - 5.
y + 1 = (-3/2)(x -1)
Change the equation y +2 = (3/2)(x - 4) into general form.
3x - 2y - 16 =0
Which astronomer is called out in “Bohemian Rhapsody”?
Galileo
A parallelogram has opposite sides equal. It is a rectangle if its angles are right angles.
To check whether ABCD is a rectangle, determine whether two intersecting sides are perpendicular.
A (-4,2), B (-3,-2), C (5,0), D (4,4)
AB =-4/1
BC = 1/4
These slopes are negative reciprocals. That means that the parallelogram is also a rectangle.An equation of a line is y = mx - (7/8). Determine
the value of m when the line passes through the
point E( -3, 5).
m = (-47/24)
Two perpendicular lines intersect on the y-axis.
One line has equation y - 3 = 2/9 (x + 5).
What does the other line look like?
y - 3 = (-9/2)
Solve the x and y intercepts for the equation
7x + 8y -56 = 0
X =8 (8,0)
Y = 7 (0,7)
What produces the majority of the breathable air on Earth?
The ocean