Chapter 5 - Straight Line Graphs

Question 1

What is the formula to calculate the gradient of a line?

Answer 1

m = (y₂ - y₁) / (x₂ - x₁)

Change in y / change in x

Question 2

How do you write the equation of a straight line?

Answer 2

y = mx + c

m is the gradient

c is the y- intercept when x = 0

It can also be written as ax + by + c = 0

Question 3

How do you find the equation of a line from a known gradient and set of coordinates?

Answer 3

y - y₁ = m (x - x₁) or m = (y - y₁) / (x - x₁)

Expand and simplify so y is the subject.

Question 4

What do parallel lines have in common?

Answer 4

They have the same gradient.

Question 5

If a line has the gradient m what would the perpendicular gradient be?

Answer 5

- 1

m

It is the negative reciprocal

Question 6

What is the product of two perpendicular lines?

Answer 6

-1

Question 7

What is the formula to find the distance between two coordinates i.e. length of line?

Answer 7

length of line between 2 coordinates:

square root of (x₂ - x₁)² + (y₂ - y₁)²

ie use pythagoras

Question 8

How do you find the point of intersection between two lines?

Answer 8

Simultaneous equations.

Solve by substitution or elimination

Question 9

When is a linear model (ie straight line) appropriate to use and when is it not?

Answer 9

It is appropriate when the points are close to the straight line ie strong positive or negative correlation. It is inappropriate the further away from the straight line the points are.

Question 10

What is the linear model used for?

Answer 10

It shows the relationship between two variables eg cost and time. It shows direct proportion (positive gradient) or indirect proportion (negative gradient).