Introduction to Graphs

A point $P$ is located on the Cartesian plane as shown in the diagram. What are the coordinates of point $P$?

If a point is at a distance of $3$ units from the $y$-axis and $4$ units from the $x$-axis in the first quadrant, what are its coordinates?

In the coordinate $(h, k)$, what is $k$ called?

The point $A(0, -4)$ lies on which axis?

Point $A$ is $(2, 0)$ and Point $B$ is $(0, 2)$. What is the shape formed by connecting $A$, $B$, and the origin $O(0, 0)$?

A line passes through the origin and the point $(4, 4)$. What is the $y$-coordinate of a point on this line whose $x$-coordinate is $10$?

The points $(1, 2)$, $(3, 2)$, and $(3, 5)$ are three vertices of a rectangle. What are the coordinates of the fourth vertex?

A line segment $GH$ is drawn such that $G$ is at $(-2, -2)$ and $H$ is at $(4, 4)$. Which of the following points lies on this line segment?

A point $M$ is such that its x-coordinate is $3$ times its y-coordinate. If the sum of its coordinates is $12$, in which quadrant does the point lie?

A circle is centered at the origin $(0,0)$ and passes through the point $(3, 0)$. Which of the following points also lies on the circle?

A student plots a linear graph using the equation $y = 2*x + 1$. Based on the graph provided, what is the value of $y$ when $x = 2$?

In a graph showing the perimeter of a square $P = 4s$, if the side $s$ is $2$ cm, what is the perimeter $P$?

Identify the $y$-coordinate of a point that lies on the $x$-axis.

What is the $x$-coordinate (abscissa) of the point $(7, 2)$?

If a line graph connects points $(1, 3)$, $(2, 6)$, $(3, 9)$, and $(4, 12)$, what is the relationship between $x$ and $y$?

Find the coordinates of the point that lies $3$ units to the left of the $y$-axis and $2$ units above the $x$-axis.

Look at the piecewise line graph. Between which two hours was there no change in the distance (the object was at rest)?

A delivery van travels from a warehouse to a retail store at a constant speed. The distance-time graph illustrates its journey. A second van leaves the same warehouse $1$ hour later and travels at a constant speed of $60$ km/h. At what distance from the warehouse will the second van overtake the first van?

The temperature of a chemical solution was recorded every hour during an experiment. The graph represents the linear cooling process of the solution. At what time (in hours) will the temperature of the solution reach $15^\circ$C?

A technician charges a fixed service fee plus an hourly rate for repairs. The relationship between the total cost ($C$ in Rs) and the time spent ($t$ in hours) is shown in the graph. If the technician worked on a machine and charged a total of Rs $550$, how many hours did the repair take?

Identify the $y$-coordinate of the point $K(5, 7)$.

What is the distance of the point $(4, 0)$ from the $y$-axis?

A point lies in the IV Quadrant. What can be said about its coordinates $(x, y)$?

In the following coordinate grid, identify the $x$-coordinate of point $M$.

The point $Q$ is $3$ units to the left of the $y$-axis and $2$ units above the $x$-axis. What are its coordinates?

What is the area of a triangle formed by the points $(0,0)$, $(4,0)$, and $(0,3)$?

A line graph shows the quantity of petrol (in liters) and its cost (in Rs). If 5 liters cost Rs 450, what is the cost of 1 liter?

A group of students tracked the water level in a reservoir during a severe summer drought. The graph shows the water level (in meters) over a period of 10 days. If the local authorities issue an 'emergency warning' once the water level stays below $15$ meters for more than $2$ consecutive days, on which day did the authorities first issue the warning based on the observed trend?

The following graph shows the variation of the side of a square and its perimeter. Is the relationship linear? If the side is $8\text{ cm}$, what is the perimeter?

The coordinates of the vertices of a triangle are $P(2, 2)$, $Q(6, 2)$, and $R(4, 6)$. What is the area of this triangle?