Ella's Blog

Arithmetic Sequences Lesson #2

Arithmetic Sequences

An arithmetic sequences in which each term is formed from the preceding term by adding a constant (positive or negative)

The Formula for the General Term of an Arithmetic Sequences.

The formula for the general term of an arithmetic sequence is

tn=t1+(n-1)d

or

tn=a+(n-1)d

Arithmetic Means

The term placed between two non-consecutive terms of an of an arithmetic sequences are called arithmetic means.

Q1. For the following arithmetic sequences:

1. Determine the common difference 2. Find the next three terms of the sequences.

A. 1. 6

2. 46, 52, 58

Equations of Linear Relations Lesson #7

Slope as a  Rate of Change

Case 1. Distance and time graph

a rate of change is a change in distance divided by a change in time.

Case 2. Temperature and time graph

a rate of change is a change in temperature divided by a change in time.

Case 3. Amount of fuel and distance travelled graph.

a rate of change is a change in the amount of fuel divided by a change in distance travelled.

Q. Taehyung is taking part in a long distance car race. After 4hours he had travelled 300km, and after 6hours he had travelled 480km.

Calculate his average speed.

A. 90km/h

Characteristics of Linear Relations Lesson #3

Slope of a Line Segment

• The slope of a line segment is a measure of the steepness of the line segment.
• It is the ratio of rise (the change in vertical height between the end points) over run (the change in horizontal length between the endpoints)

Slope formula

Slope = rise/run = change y/change x= y1-y2/x1-x2

★ The rise is POSITIVE if we count UP↑, and NEGATIVE if we count Down↓

The run is POSITIVE if we count RIGHT→, and NEGATIVE if we count LEFT←

Q. Calculate the slope of (1,3) and (4,9)

A. Slope = 2

Equations of Linear Relations Lesson #3

Writing Equations using y – y1 = m(x – x1)

• To determine the equation of a line in future math courses, the point – slope equation, y – y1 = m(x – x1), is used more frequently than the slope – y – intercept equation, y = mx + b.

Q. The slope of a line end a point on the line are given. Determine the equation of the line in slope y-intercept form.

A. y= 2/3x – 12

Equations of Linear Relations Lesson #4

The General Form Equation Ax + By + C =0

• Given the equation of a line in general form, Ax + By +  C =0, the slope and y – intercept can be found by converting the equation into slope y – intercept form, y = mx + b.

Ex) 2x – 3y + 12 =0

2x : always positive

2x – 3y + 12 : all integer values

Q. Determine the equation of a line which is perpendicular to the line 2x – 6y + 6 =0 and has same y-intercept.

A. 3x + y – 1 =0

Characteristics of Linear Relations Lesson#2

The distance Formula

Distance on a coordinate plane.

Distance: Subtraction

(difference in x-coordinates of B and A)^2+(difference in y-coordinates of B and A)^2

d=√(x2-x1)^2+(y2-y1)^2

Q1. Determine the distance between each pair of points.

√232 =2√58