Straight line graphs

Question 1

How can the gradient m of the line joining the points (x₁, y₁) and (x₂, y₂) be calculated?

Answer 1

m = (y₂ - y₁) / (x₂ - x₁)

This formula calculates the slope of the line between two points.

Question 2

What is the general form of the equation of a straight line?

Answer 2

y = mx + c

Here, m is the gradient and (0, c) is the y-intercept.

Question 3

What is another form of the equation of a straight line?

Answer 3

ax + by + c = 0

In this form, a, b, and c are integers.

Question 4

What is true about the gradients of parallel lines?

Answer 4

Parallel lines have the same gradient.

This means they will never intersect.

Question 5

What is the relationship between the gradients of two perpendicular lines?

Answer 5

The product of their gradients is -1.

If one line has a gradient m, the perpendicular line has a gradient of -1/m.

Question 6

What is the equation of a line with gradient m that passes through the point (x₁, y₁)?

Answer 6

y - y₁ = m(x - x₁)

This form is derived from point-slope form of a line.

Question 7

How can the distance d between points (x₁, y₁) and (x₂, y₂) be calculated?

Answer 7

d = √((x₂ - x₁)² + (y₂ - y₁)²)

This formula is derived from the Pythagorean theorem.

Question 8

How can the point of intersection of two lines be found?

Answer 8

Using simultaneous equations.

This involves solving the equations of the two lines together.

Question 9

What characterizes two quantities in direct proportion?

Answer 9

They increase at the same rate.

Graphically, this relationship is represented by a straight line through the origin. y = x

Question 10

What does V = mx + c represent?

Answer 10

A linear relationship in direct proportion.

This is a specific application of the straight line equation.

Question 11

What is a mathematical model?

Answer 11

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

Creating a model often requires making assumptions about real-life problems.