Slope of a Line

Use concept of slope to prove following points are collinear.

$\left(0,2\right),\left(1,5\right),\left(-2,-4\right) \& \left(-6,-16\right)$

Use concept of slope to prove following points are collinear.

$\left(4,2\right),\left(5,4\right),\left(2,-2\right) \& \left(3,0\right)$

Use concept of slope to prove following points are collinear.

$\left(4,8\right),\left(5,12\right),\left(9,28\right) \& \left(11,36\right)$

The coordinates of point $P$ are $\left(-3, 8\right)$ and the coordinates of point $Q$ are $\left(5, 3\right)$. $M$ is the midpoint of $\left[PQ\right]$.

$L_1$ is the line which passes through $P$ and $Q$.

Find the gradient of $L_1$.

The ski slopes in the Scotch Pine Ski Resort are marked by colour as an indicator of the incline. The colours used are green, blue, red and black. Green is used for slopes with less than $20\%$ incline, blue for $20-25\%$, red for $25-40\%$ and black for above $40\%$ incline.

If the slopes are given as follows:

$P_1$ with a horizontal change of $450 m$ and a vertical change of $280 m$ that passes through $O\left(0,0\right)$.

$P_2$ with a horizontal change of $150 m$ and a vertical change of $50 m$ that passes through $O\left(0,0\right)$.

$P_3$ with a starting point at the top ${\mathrm{B}}_1(310,48)$, and an end at $O\left(0,0\right)$.

$P_4$ with a starting point at the top ${\mathrm{B}}_2(230,56)$ and an end at $O\left(0,0\right)$.

On a pair of axes, graph each line, label it, and mark it with the respective colour.

The ski slopes in the Scotch Pine Ski Resort are marked by colour as an indicator of the incline. The colours used are green, blue, red and black. Green is used for slopes with less than $20\%$ incline, blue for $20-25\%$, red for $25-40\%$ and black for above $40\%$ incline.

If slope $P_2$ with a horizontal change of $150 m$ and a vertical change of $50 m$ that passes through $O\left(0,0\right)$. Determine the angle of inclination, $\alpha$, of slope $P_2$.

The ski slopes in the Scotch Pine Ski Resort are marked by colour as an indicator of the incline. The colours used are green, blue, red and black. Green is used for slopes with less than $20\%$ incline, blue for $20-25\%$, red for $25-40\%$ and black for above $40\%$ incline.

Classify the following slopes as blue, green, red or black:

$P_4$ with a starting point at the top ${\mathrm{B}}_2(230,56)$ and an end at $O\left(0,0\right)$.

The ski slopes in the Scotch Pine Ski Resort are marked by colour as an indicator of the incline. The colours used are green, blue, red and black. Green is used for slopes with less than $20\%$ incline, blue for $20-25\%$, red for $25-40\%$ and black for above $40\%$ incline.

Classify the following slopes as blue, green, red or black:

$P_3$ with a starting point at the top ${\mathrm{B}}_1(310,48)$ and an end at $O\left(0,0\right)$.

The ski slopes in the Scotch Pine Ski Resort are marked by colour as an indicator of the incline. The colours used are green, blue, red and black. Green is used for slopes with less than $20\%$ incline, blue for $20-25\%$, red for $25-40\%$ and black for above $40\%$ incline.

Classify the following slopes as blue, green, red or black:

$P_2$ with a horizontal change of $150 m$ and a vertical change of $50 m$ that passes through $O\left(0,0\right)$.

The ski slopes in the Scotch Pine Ski Resort are marked by colour as an indicator of the incline. The colours used are green, blue, red and black. Green is used for slopes with less than $20\%$ incline, blue for $20-25\%$, red for $25-40\%$ and black for above $40\%$ incline.

Classify the following slopes as blue, green, red or black:

$P_1$ with a horizontal change of $450 m$ and a vertical change of $280 m$ that passes through $O\left(0,0\right)$.

Road signs showing the steepness of hills are often given as percentages, as in the one shown below,

Determine the vertical change corresponding to a horizontal change of $5 km$ for a road with sign indicating $15\%$ incline.

Road signs showing the steepness of hills are often given as percentages, as in the one shown below,

Which is the steeper road-the one with a sign indicating $10\%$ incline or another with a sign indicating $15\%$?

Road signs showing the steepness of hills are often given as percentages, as in the one shown below,

For a certain road the vertical change is $5 m$ for a horizontal change of $20 m$. Determine the percentage that would be written on the sign for this road.

US roof regulations state that asphalt tiles can only be used for roofs with a minimum gradient of $0.17$. The roof shown in the diagram has width $7m$, and rise $1.6m$.

Determine whether the roof satisfies the requirements for using asphalt tiles. Justify your conclusion.

US roof regulations state that asphalt tiles can only be used for roofs with a minimum gradient of $0.17$. The roof shown in the diagram has width $7m$, and rise $1.6m$. Find the roof gradient,

A town website advertises summer jobs for students. A student is trying to decide between a job as a city guide and a job at a flower shop. The job as a city guide pays $\$40$ per day plus a monthly metro card with $\$120$ value. The job at the flower shop pays $\$60$ a day. Compare the payments for the two jobs.

Explain how the student should decide which job to take based on the number of days they plan to work during the month.

A town website advertises summer jobs for students. A student is trying to decide between a job as a city guide and a job at a flower shop. The job as a city guide pays $\$40$ per day plus a monthly metro card with $\$120$ value. The job at the flower shop pays $\$60$ a day. Compare the payments for the two jobs.

Draw the lines representing the payments for each job. On the same pair of axes, where $x$ is the number of days worked and $y$ is the payment in dollars.

A town website advertises summer jobs for students. A student is trying to decide between a job as a city guide and a job at a flower shop. The job as a city guide pays $\$40$ per day plus a monthly metro card with $\$120$ value. The job at the flower shop pays $\$60$ a day. Compare the payments for the two jobs.

Complete the table below:

$\begin{array}{|ccc|}\hline \begin{array}{c}\text{ Number of }\\ \text{ days worked }\end{array}& \begin{array}{c}\text{ City guide }\\ \text{ [USD] }\end{array}& \begin{array}{c}\text{ Flower shop }\\ \text{ (USD) }\end{array}\\ 1& 160& 60\\ 5& & \\ 10& & \\ \hline\end{array}$

MegaLift plans ski slopes and lift stations along the slopes. Find the height of a ski lift station $B\left(490,h\right)$, which is on a slope with gradient $0.35$ and which passes through a lower lift ski station $A\left(90,10\right)$. All coordinates are given in metres.

A skier travels downhill along two slopes: one with gradient $-3$ and the other with gradient $\frac{-1}{3}$. State which slope is the, steeper, justifying your answer.