Topic 2.1: Linear Models Questions

What is the gradient of a line perpendicular to y = (1/2)x + 3?

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

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

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

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.

The gradient of the line through (2, 5) and (6, 13) is

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

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

Which line has a gradient of zero?

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

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

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

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

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

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

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

A gym charges $50 to join and $30 per month. Which model gives the total cost C after m months?

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

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]

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