Equations of straight lines (AASL2.1)

Keywords

English	Japanese	Korean	Chinese Simplified
Standard Equation of a Line	直線の標準方程式	직선의 표준 방정식	直线的标准方程
Parallel Lines	平行線	평행선	平行线
Perpendicular Lines	垂直線	수직선	垂直线
Slope	傾き	기울기	斜率
Parallelism	平行性	평행성	平行性
Perpendicularity	垂直性	수직성	垂直性
Slope-intercept Form	傾き-切片形式	기울기-절편 형식	斜截式
y-intercept	y切片	y-절편	y轴截距
Coefficients	係数	계수	系数
General Form Equation	一般形式方程式	일반 형식 방정식	一般形式方程
Line Steepness	線の急斜度	선의 가파름	线的陡峭度
Horizontal Lines	水平線	수평선	水平线
Vertical Lines	垂直線	수직선	垂直线
Perpendicular Slope	垂直線の傾き	수직선의 기울기	垂直斜率

Inquiry questions

Factual Inquiry Questions	Conceptual Inquiry Questions	Debatable Inquiry Questions
What is the standard form of the equation of a straight line?	Why does the slope play a crucial role in determining the parallelism or perpendicularity of two lines?	Is the concept of parallel and perpendicular lines more significant in geometry than in practical applications, or vice versa?
How can you determine if two lines are parallel or perpendicular based on their equations?	How can the equations of parallel and perpendicular lines be derived from a given line equation?	Can the mathematical principles of parallel and perpendicular lines be applied to conceptualize ideas in modern physics and cosmology?
		How do the concepts of parallelism and perpendicularity in straight lines influence architectural design and urban planning?

Exploring the Slope (m) Move point A vertically up and down. How does this affect the slope (m) of the line? Does the slope increase or decrease as you move A up or down? Move point B horizontally left and right. How does this movement change the slope? What happens to the slope if B moves further away from the y-axis?

Intercept (c) Exploration Keep the slope constant and move point A horizontally left and right. How does this affect the y-intercept (c)? Does the intercept increase or decrease as A moves? What happens to the y-intercept if you keep point A fixed at the y-axis and only move point B along the line?

Exploring Slopes of Parallel Lines Adjust point A along the red line and point C along the blue line. Observe how the slopes of both lines remain constant despite the movement of these points. What does this tell you about the slopes of parallel lines? How do the equations of the red and blue lines change as you move points A and C? What remains constant, and what can change while maintaining parallelism?

Understanding Y-Intercepts of Parallel Lines Move point B vertically. Note how the y-intercept of the red line changes. Can you move point B to make the two lines intersect, or do they remain parallel regardless of the y-intercept? Examine the relationship between the y-intercepts of the two lines. When the slopes are the same, how do different y-intercepts affect the distance between the two lines?

Horizontal Lines Investigation Can you manipulate points A, B, and C to create horizontal lines? What would the slope of a horizontal line be, and how would you represent it in slope-intercept form? If you have two horizontal lines, what must be true about their y-intercepts if they are to remain parallel?

Effects on the General Form Coefficients (a, b, and c) As you move point A, observe how coefficients 'a' and 'b' in the general form change. Is there a consistent pattern between the changes in 'a' and 'b' and the movements of A? Move point B while keeping A stationary. How do the coefficients 'a', 'b', and 'c' change? Can you establish a relationship between these changes and the position of B?

The General Form - ax+by+c - Puzzle

Using only the digits 0-9 once each, can you find a solution to create two parallel lines?

Part 3 - Perpendicular lines

Investigating the slope of perpendicular lines

Investigating Slope Ratios

Change the gradient of one line using the slider. What happens to the gradient of the perpendicular line? How does the ratio between the two gradients change?

Exploring Slope Signs Observe the signs of the gradients as you adjust the slider. If one line has a positive gradient, what can you infer about the gradient of the perpendicular line?

Slider Position and Line Steepness As you move the slider from one end to the other, note the steepness of each line. How does the steepness of one line relate to the steepness of the line perpendicular to it?

Try to create a horizontal line. What is the slope of the perpendicular line? Similarly, try to adjust the slider to create a vertical line. What do you observe about the slope of the line perpendicular to it?