AS Pure Chapter 5: Straight Line Graphs

7 flashcards · Mathematics · by TheoTyson

1. Calculate the gradient of the line connecting points (x1,y1)(x_1, y_1)(x1​,y1​) and (x2,y2)(x_2, y_2)(x2​,y2​) .

   m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}m=x2​−x1​y2​−y1​​

2. What is the equation of a straight line?

   y=mx+cy = mx + cy=mx+c where ccc is the yyy -intercept.

3. What is the equation of a straight line with a gradient mmm that passes through the point (x1,y1)(x_1, y_1)(x1​,y1​) .

   y−y1=m(x−x1)y - y_1 = m(x - x_1)y−y1​=m(x−x1​)

4. What is the relationship between parallel lines?

   They have the same gradient.

5. If a line has a gradient mmm , what is the gradient of a perpendicular line?

   −1m- \frac{1}{m}−m1​

6. What is the product of the gradients of two lines that are perpendicular?

   −1-1−1

7. What is the distance between two points (x1,y1)(x_1, y_1)(x1​,y1​) and (x2,y2)(x_2, y_2)(x2​,y2​) ?

   d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}d=(x2​−x1​)2+(y2​−y1​)2 ​