Topic 2.1: Linear Models Questions

The diagram shows the linear model P = 4t + 20 for the number of plants in a garden after t weeks. Interpret the gradient and y-intercept of this model.

[Diagram: x-axis from 0 to 10 y-axis from 0 to 60 A(0, 20) B(10, 60) joined by a straight line L]

Line L₁: y = 4x − 3. Line L₂: y = 4x + 7. State two geometric properties of these lines.

A line has gradient −2 and passes through the point (0, 5). Write the equation of the line.

The diagram shows a straight line passing through points A(−2, 1) and B(4, 13). Find the gradient of the line.

[Diagram: coordinate grid with x-axis from −4 to 6 and y-axis from −3 to 15. Points A(−2, 1) and B(4, 13) are plotted and joined by a straight line L.]

A line has gradient 3 and y-intercept −5. Its equation is

Write down the gradient and y-intercept of the line y = −(1/3)x + 9.

A car is worth $18 000 when bought and loses value at $1500 per year. What is the value after 4 years?

A mobile data plan costs $25 per month plus $0.05 per MB used. Write the monthly cost model C in terms of MB used (n), and find the cost for 400 MB.

Which line has a gradient of zero?

Show that its gradient is $2$.

Lines L₁: y = ax + 3 and L₂: y = 4x − 1 are parallel. Find the value of a.

Which line is parallel to y = −3x + 7?

Write down the gradient and y-intercept of y = −2x + 7.

Find the equation of the line with gradient −3 that passes through (1, 4).

The model T = −2h + 20 gives temperature T (°C) at altitude h (km). What does the −2 represent?

What is the y-intercept of the line y = 7x − 4?

A straight line passes through (0, −6) and has gradient 3. On the diagram, sketch the line, labelling the gradient and y-intercept.
[Diagram: x-axis from -2 to 4 y-axis from -8 to 6 sketch:line gradient=3 y-intercept=-6]

Find the gradient of the line joining (1, 4) and (5, 16).

Find the equation of the line parallel to y = 5x − 2 through (1, 8).

A line has gradient 4 and passes through (0, −3). Write down its equation.