Linear Algebra

Linear Inequalities

100

What does > and < mean

> means greater than

< means lesser than

200

Solve x−5<10

x<15

300

Graph the inequality x≤−1

Closed circle at -1, shade left

400

Solve −2x≤10

x≥−5 

The sign flips when multiplying or dividing by a negative number.

500

Show the number line and state linear inequality for a number that is at least 2 but less than 9

2≤x<9

Equations of Lines

100

Is the slope y=4x−1 increasing or decreasing

The gradient is 4, therefore it is increasing.

200

Find the equation of the line with gradient 2 and y-intercept of 4

y=2x+4

300

A line crosses the y-axis at −6 and rises 6 for every run of 3. Write its equation.

y=2x-6

400

Two points on a line are (-2, 9) and (4, -3). Find the equation of the line.

Gradient =(9--3/-2-4)

             =(12/ -6)

             =(-2)

Y-Intercept= 9=-2 x -2 + c

                = 9=4 + c

                = 5=c

y=-2x+5

500

Create a real-life situation that could be modeled by the equation y=4x

Needs to increase by 4 for every time 1 think happens. 

e.g. buying cans of drinks for $4 each

Length

100

How do you find the distance between two points on a coordinate plane

d=square root of (x₂-x₁)+(y₂-y₁)

200

Find the distance between (1,1) and (1,6)

5

300

What is the first step in the distance formula?

Label your coordinates

400

Find the distance between (−3,4) and (5,−2)

10

500

A point is 10 units from another point, and the horizontal difference is 2. Find the vertical difference (leave as square root)

2² + vertical² =10²

4 + vertical² =100

        vertical² =96

Answer is the square root of 96

Midpoint

100

Explain what is midpoint and its formula.

It is in middle between two endpoints on a line segment. It is found by finding the average of the x and y points. M=((x1+x2)/2), ((y1+y2)/2)

200

Find the midpoint of (2,6) and (8,10)

(5, 8)

300

Find the midpoint of (−6,5) and (10,−3)

(2, 1)

400

A line segment has endpoints (x,5) and (9,−1), and its midpoint is (4,2). Find x

x=-1

500

The midpoint of a segment is (3,−2). One endpoint is (−1,4). Find the other endpoint.

(7, -8)

Perpendicular + Parallel Lines

100

Explain the gradient for both parallel and perpendicular lines. 

The gradient for parallel lines is the same. The gradient for perpendicular lines is the negative reciprocal.

200

Name another equation of line that is parallel to y=5x-7

Anything as long as it has a gradient of 5

300

Find the perpendicular slope of m=−3m

m=1/3

400

Find the equation of a line parallel to y=3x−4 passing through (2,5)

y=3x-1

500

Find the equation of a line perpendicular to y=−2x+7 passing through (1,−3)

y=1/2 x - 7/2 

OR 

y=1/2 x - 3.5