Baldwin Street in Dunedin, New Zealand, is known as the steepest street in the world. Baldwin Street is a short residential street about $350$ metres long. From its base at approximately $30$ metres above sea level, it rises to a height of about $100 \mathrm{m}$ above sea level. The segment shown in the following diagram models Baldwin Street.

Find the grade of Baldwin street.

Determine whether lines $1$ and $2$ which pass through the given points are parallel, perpendicular or neither.

Line $1:(3,6) \& (6,11)$

Line $2:(4,-1) \& (9,2)$

Determine whether lines $1$ and $2$ which pass through the given points are parallel, perpendicular or neither.

Line $1:(5,-1) \& (3,7)$

Line $2:(-1,4) \& (0,0)$

A line passes through the points $(3,2)$ and $\left(x,5\right)$ and is perpendicular to a line with gradient $\frac{4}{3}$. Find the value of $x$.

Liam works up to $60$ hours each week. His weekly pay, in dollars, depends on the number of hours he works, as shown in the graph.

Find the gradient for each line segment in the graph.

Liam works up to $60$ hours each week. His weekly pay, in dollars, depends on the number of hours he works, as shown in the graph.

Explain the meaning of each gradient in the context of Liam's work.

Write down the gradient and $y-$intercept for the following line:

$y=3x-7$

Write down the gradient and $y-$intercept for the following line:

$y=-\frac{2}{3}x+4$

Write down the gradient and $y-$intercept for the following line:

$y=-2$