Construct a straight-line graph using a linear function of the form, 𝑦 = 𝑚𝑥 + 𝑐 where 𝑚 is slope (gradient) and 𝑐 is 𝑦-intercept.

A landscape designer plans a walkway that increases in elevation at a constant rate. For every 3 metres of horizontal distance, the walkway rises 2 metres vertically. The walkway starts at ground level (height 0 metres). Which of the following represents the relationship between horizontal distance \(d\) (metres) and height \(h\) (metres)?

A heating engineer charges a call-out fee plus an hourly rate for each job. The table below shows the total cost for jobs of different durations. Construct a straight-line graph to display the relationship between job duration and total cost on the grid provided, showing: (a) the linear function in the form \(y = mx + c\) [2 marks] (b) the graph with appropriate scaling and labelling of axes [2 marks]

A landscaper charges clients using the linear function $y = 45x + 120$, where $x$ is the number of hours worked and $y$ is the total cost in dollars. (a) Identify the gradient and the $y$-intercept of this function. (1 mark) (b) State the coordinates of two points that lie on this line. (1 mark) (c) Use your answers from parts (a) and (b) to describe how you would construct the straight-line graph of this function on a coordinate grid. (1 mark)