Linear relationships

Question 1

Graphing linear functions

Answer 1

1. Construct a table of values with the independent variable as the first row and the dependent variable as the second row.
2. Draw a number plane with the independent variable on the horizontal axis and the dependent variable on the vertical axis. Plot the points.
3. Join the points to make a straight line.

Question 2

Gradient and intercept

Answer 2

Gradient of a line is the slope of the line.
The intercept of a line is where the line cuts the axis.
Gradient (or m) = Vertical rise OVER Horizontal run

Question 3

Gradient–intercept - formula

Answer 3

Linear equation in the form y = mx + b.
m – Slope or gradient of the line.
b – y-intercept.
Sketching a straight-line graph requires at least two points. When an equation is written in gradient–intercept form, one point on the graph is immediately available: the y-intercept. A second point can be calculated using the gradient.

Question 4

Linear models

Answer 4

Linear modelling occurs when a practical situation is described mathematically using a linear function.

Question 5

Direct variation

Answer 5

1. Write an equation relating the two variables, using k is the constant of variation.
   When y is directly proportional to x the equation is y = kx.
2. Solve the equation for k by substituting values for x and y.
3. Write the equation with the solution for k (step 2) and solve the problem by substituting a value for either x or y.