EDEXCEL A-LEVEL PURE MATHS (5): STRAIGHT LINE GRAPHS

How can you find the gradient of a straight line joining two points?

- By considering the vertical distance and the horizontal distance between the points.

- The gradient, m, of a line joining the point with coordinates (x₁, y₁) to the point with coordinates (x₂, y₂) can be calculated using the formula:

m = (y₂ - y₁) ÷ (x₂ - x₁).

What are some examples of finding the gradient of a straight line joining two points?

What are the two forms the equation of a straight line can be written in?

- y = mx + c, where m is the gradient and c is the y-intercept.

- ax + by + c = 0, where a, b and c are integers.

What are some examples of rearranging the equations of straight lines into different forms?

What is an example of deducing the coordinates of a point with the equation of a straight line?

How can a the equation of a straight line be found?

You can define a straight line by giving:

- One point on the line and the gradient.

- Two different points on the line.

How can the equation of the line with a gradient, m, that passes through the point with coordinates (x₁, y₁) be written?

y - y₁ = m(x - x₁)

What are some examples of finding the equation of a line using y - y₁ = m(x - x₁)?

What are some examples of finding the equation of a line using y - y₁ = m(x - x₁) and also writing your answer in a different form?

What are some examples of finding the equation of a line from two simultaneous equations and using y - y₁ = m(x - x₁); and also writing your answer in a different form?

How do you know if two lines are parallel and what is an example of working out the equation of a parallel line when given the equation of a line and point it passes through?

What are perpendicular lines?

- Perpendicular lines are at right angles to each other.

- If you know the gradient of one line, you can find the gradient of the other.

- If a line has a gradient of m, a line perpendicular to it has a gradient of -1/m.

- If two lines are perpendicular, the product of their gradients is -1.

How can you find the equation of a line when given the equation of a line that is perpendicular to it, and a point that the perpendicular line passes through?

How can you find the distance between two points?

- You can find the distance between two points A and B by considering a right-angled triangle with hypotenuse AB.

- You can find the distance, d, between (x₁, y₁) and (x₂, y₂) by using the formula:

d = √(x₂ - x₁)² ÷ (y₂ - y₁)².

What is an example of finding the distance between two points?

What is an example of a problem involving two straight lines, coordinates and the area of a triangle?

How can straight line graphs model direct proportion?

How can the extenstion of a spring with different masses be modelled with straight line graphs?

What are linear models?

- You can sometimes use a linear model to show the relationship between two variables, x and y.

- The graph of a linear model is a straight line, and the variables are related by an equation of the form y = ax + b.

- The linear model can still be appropriate even if all the points don't lie directly on the line, in which case the points should be close to the line.

- The furthe the points are from the line, the less appropriate a linear model is for the data.

What is a mathematical model?

- An attempt to represent a real-life situation using mathematical concepts.

- It's often neccessary to make assumptions about the real-life problem in order to create a model.

What is an example of a problem involving linear models?

What is another example of a problem involving linear models?

EDEXCEL A-LEVEL PURE MATHS CHAPTER FIVE: STRAIGHT LINE GRAPHS

(MAKE SURE YOU KNOW THE FOLLOWING)