Circles
Parallel/Perpendicular Lines
Midpoint
Mixed Equations
Slope
100
The equation for circle A is x2 + y2 = 13. Does the point (2,3) fit on this circle.
YES! 4 + 9 = 13
100
How can you tell if two equations would be parallel?
The slopes are the same!
100
What is the midpoint formula?
x1 + x2 y1 + y2 ---------- , ------------ 2 2
100
Plug in the value for x and solve! 4x + 3 x = -5
-17
100
1. How can you identify the slope in an equation? 2. How can you find the slope on a graph?
1. The number with the x. 2. rise y2 - y1 ------ ---------- run x2 - x1
200
Write an equation for a circle whose radius is 5.
x2 + y2 = 25
200
What do you know about the slopes of perpendicular lines?
The slopes are negative reciprocals!
200
Find the midpoint of the two points below. (2,3) (5,5)
(3.5, 4)
200
Solve for x. 2x + 3 = 7
x = 2
200
Find the slope in the equation below. y = -3x - 2
slope = -3
300
The equation for a drawn circle is x2 + y2 = 25. Write an equation for a point OUTSIDE the circle.
What is x2 + y2 > 25
300
Would the two lines below be perpendicular? y= 4x +2 y = -4x +2
NO! Slope is not the negative reciprocal.
300
Find the midpoint of the points below. (11,21) (12,29)
(11.5, 25)
300
Solve for s. 4s = 6s +2
s = -1
300
Find the slope. (-2,3) (5, -5)
slope = -8/7
400
The equation for a drawn circle is x2 + y2 = 25. Write an equation for a point in the interior of the circle.
x2 + y2 < 25
400
Bailey wrote two equations and wrote whether they were parallel or perpendicular but then Jack ate the corner of her page! What should Bailey have written about the two equations below? y = 4x + 21 y = 4x -5
The two equations are parallel because the slopes are the same. P.S. My precious Jack would never do such a thing :)
400
Your teacher will give you a graph showing a line. Find the midpoint between the two points shown.
(2,3)
400
2x + 16 = 7x +1 Solve for x!
x = 3
400
Find the slope. (10, 24) (10, 1)
Slope = undefined
500
Find the area and circumference of a circle with a diameter of 8.
A = 50.24 u2 C = 25.12 u
500
Write equations that are parellel and perpendicular to the equation below. **HINT: Make sure it is in slope-intercept form (y = mx + b) 2y = 4x +10
2y = 4x +10 = y = 2x+5 (slope-intercept form) Parallel: Any equation with the slope of 2. Perpendicular: Any equation with the slope of -1/2.
500
Find the coordinates of the midpoint of (-5,3) and (13, -17).
(4, -7)
500
4 (x + 5) = 6(x + 4)
x = -2
500
Find the slope (-3, -5) (3, 7)
slope = 2
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