Linear Algebra & Graphs

Solving by Collecting Like Terms

100

5h + 2 + 2h = 23

h = 3

200

3b + b - 8 = 4

b = 3

300

3a + 12 - 6a = -9

a = 7

400

-6 = -3y + 4 + 5y

y = -5

500

78 = 3c + 12 - c + 4

c = 31

Solving by Using the Distributive Law

100

2(x + 5) = 14

x = 2

200

5(d - 2) = 40

d = 10

300

7(4 - t) = -84

t = 16

400

-2(x - 9) = -24

x = 21

500

-13(4 + 2a) = 208

a = -10

Equation of the Line

100

In the standard formula for the equation of the line (y=mx+c) what do the following letters each represent?

y=y co-ordinate

m= gradient/slope/rate of change

x=x co-ordinate

c=y-intercept (when x=0)

200

Find the equation of the line with gradient -3 and a point that passes through (0, 6)

y=-3x+6

300

Write down the gradient and y-intercept of the straight line with equation 3𝑦 = 2𝑥 − 9

m=2/3 & c=-9/3 or -3

400

Find the equation of the line that passes through (0, 10) and (5, 30). Give your answer in the form y=mx+c.

y=4x+10

500

Find an equation of the line that passes through the points (4, 2) and (−8, 11). Give your answer in the form y=mx+c.

y= -3/4x+5

Gradient

100

Fill in the blank: The gradient is a measure of ____?

Slope/Rate of change as x increases by 1 

200

A gradient that is deemed to be 'undefined', is set to have what as 0?

Denominator/Run/Change in x

300

Find the gradient of the straight line that passes through points: (2, 4) and (-2, 16)

m=-3

400

A line with gradient -2 passes through the points (5, 5) and (b, 9). Find the value of b.

b=3

500

Find the gradient of the line joining the points (4, 5) and (6, 5). What is the equation of this line?

gradient=0 

y=5 (Straight Line)

Word Problems

100

WRITE AN EQUATION & SOLVE: Julie is 3 years older than her sister. Julie's age is 11 years old. How old is her sister?

n - Julie's sister's age n + 3 = 11 n = 8 Julie's sister is 8 years old.

200

Rule for distance travelled over a given time for a car is given by d=50+80t where d (km) and t (hours). For a 2 hour journey from Melbourne to Sydney, how far has the car travelled?

50+80(2)=160+50=210km

300

Tyler has 4 boxes of apples. Each box has the same number of apples. After Tyler eats 3 apples, there are 109 apples left in the boxes. How many apples were in each box?

a - # of apples in each box 4a - 3 = 109 a = 28 There were 28 apples in each box.

400

The water level (cm) in a dam starts at 300cm and decreases by 5 cm everyday for 10 days. Mr G confidently feels the equation should be h=300t-5. But his answer is wrong. What would be the correct rule for this relationship.

h=-5t+300

500

When you count by ones fron many integer, you are counting consecutive integers. Using variables, three consecutive integers are n, n + 1, and n + 2. The sum of three consecutive integers is 48. What are the integers?

n + n + 1 + n + 2 = 48 n = 15 The integers are 15, 16, and 17.