3 Jan/Feb Flashcards
Coordinates, Linear graphs, Ration and proportion, Pythagoras, Trigonometry, Indices
Negative Gradient
The line goes down from left to right.
Gradient
Y₂ -Y₁
_____
X₂ - X₁
Change in x
Perpendicular lines have gradients which ________ together to give _.
1) multiply
2) -1
The gradient of the perpendicular line is…
…the negative reciprocal of the gradient of the original line.
Q: Gradient = m. What is the perpendicular gradient?
m = m/1
A: -1/m
Q: Gradient = 1/m. What is the perpendicular gradient?
-m/1
A: -m
Q: Gradient = m/n. What is the perpendicular gradient?
A: -n/m
Midpoint of a line
(Xᴀ+Xʙ /2 , Yᴀ+Yʙ / 2)
Q: Find the equation of a line parallel to y=3x-2 and goes through (4,6).
y=3x+c = (parallel line) Substitute: when x=4, y=6 6 = (3*4) + c = 12+c 6= 12 + -c 6 = 12 + -6 = 12 - 6 c = -6 A: y = 3x - 6
Q: Find the equation of the line perpendicular to lie y=2x+5 and goes through (-2,7).
y = -½x + c (perpendicular: negative reciprocal) When x=-2, y=7 7=(-½ * -2) + c = 1 + c c = 7-1 = 6 A: y = -½x + 6
Put the following ratios in their simplest form:
1) 30:18
2) 6:15
3) 8:28
4) 12:32
5) 35:28
1) 5:3
2) 2:5
3) 2:7
4) 3:8
5) 5:4
Q: In my house, the ratio of dogs to fish is 1:10. The ratio of fish to cats is 6:1. What is the ratio of dogs to cats?
f = 10*6 = 60 d = 1 } 1*6 = 6 c = 1 } 1*10 = 10 d : f : c = 6 : 60 : 10 d : c = 6 : 10 A: 3 : 5
Direct proportion
y α x
y = kx
Inverse proportion
y α 1/x
y = k/x
Q: 4 pizzas cost 𝘹 pounds. How much do 𝘺 pizzas cost, in pounds?
p α m = p = km 4 = kx } k = 4/x y = k * m = 4/x * m m = y ÷ 4/x m = y/1 * x/4 = yx/4 A: xy/4
