Basic Questions with Simple Graphs
In the following graph one point on the function is marked. According to the graph, what is the X value of the point?
The point is above the marking for the number 2 on the X axis, so X = 2.
In the following graph one point is marked. What is the X value of the point?
The point is above the number 3 on the X axis, so X = 3.
The following graph shows a rising straight line. Which equation fits the general form of the line (linear relationship between X and Y)?
A rising straight line corresponds to a linear equation of the form Y = aX + b.
The following graph shows a constant function (horizontal straight line). Which equation fits this description?
A horizontal line represents a constant function: Y equals a constant number that does not depend on X.
The following graph marks a point that represents the solution of a single-variable equation. What is true about the point?
In a graph, the solution of an equation is typically represented by the X value where the line or point is located.
The following graph marks only one point. What can we say about the equation describing the relationship between X and Y?
A single point can fit infinitely many lines, so it is not enough to determine a unique line equation.
The following graph marks a point that lies on the X axis. What is the Y value of that point?
A point on the X axis is a point where Y equals zero.
The following graph marks a point that lies on the Y axis. What is the X value of that point?
A point on the Y axis is a point where X equals zero.
The following graph shows a straight line crossing the Y axis at a marked point. What does the Y intercept represent in the equation of the line?
In the linear equation Y = aX + b, the Y intercept is the value b.
The following graph shows a straight line crossing the X axis at a certain point. What does the X value at that point represent?
When the line crosses the X axis, the X value at that point is the solution satisfying Y = 0 in the equation.
The following graph marks a point where the Y value is positive. What can be inferred about the location of the point?
A positive Y value means the point is located above the X axis.
The following graph shows a falling straight line. What can be inferred about the slope?
A falling line is a line with a negative slope.
What is the X value of the blue point?
The point is positioned above the marking for 3 on the X axis.
What is the Y value of the point?
The point is at the height of the Y marking labelled 2.
Which of the options describes a horizontal line?
A horizontal line is a constant function: Y = c.
The following graph shows a line with a large slope. What does this mean?
A high slope = a steep rise.
What is the X value where the line crosses the X axis?
The intersection point is at an X value close to 3.
The following graph shows a point exactly on the Y axis. What is the X value?
A point on the Y axis → X value = 0.
The following graph shows a straight line. What can be said about the relationship between X and Y?
A straight line represents a linear relationship.
Which point on the graph corresponds to a negative Y value?
Negative Y → below the X axis → the red point.
The point in the graph is marked below the X axis. What can be inferred about the Y value?
A point below the X axis → negative Y value.
The following graph shows a nearly horizontal line. What does this say about the slope?
A nearly horizontal line indicates a small slope.
Which point is marked on the X axis?
A point on the X axis is at Y = 0 (in our graph Y=0 is represented by the bottom line).
The following graph contains a straight line. How can we tell it is not horizontal?
A line that is not parallel to the X axis → its slope ≠ 0.
The following graph marks a point exactly at the intersection of the two axes. What are the values of the point?
The intersection of the two axes is the origin: (0,0).
What is the Y value of the blue point?
The point is at the height of the Y marking labelled 1.
The following graph shows a straight line with a positive slope. What does this type of slope mean?
Positive slope = Y rises as X rises.
The following point is located to the right of the Y axis. What can be inferred about the X value?
A point to the right of the Y axis → positive X value.
Which point represents a negative X value?
To the left of the Y axis → negative X value.
The point is marked on the line. What is true about its X and Y values?
If the point is on the line — it satisfies the equation.
What can be said about the point when it is exactly on the Y axis?
A point on the Y axis → X value is zero.
The following graph shows a straight falling line. What type of slope does it have?
A falling line = negative slope.
The point is marked to the left of the Y axis and below the X axis. What can be inferred?
Left of the Y axis → X negative; below the X axis → Y negative.
Which point indicates a positive Y value and a negative X value?
Above the X axis → Y positive; left of the Y axis → X negative.
In the following graph, which X values are valid for the line shown?
The line is continuous, so all X values in the graph domain are valid.
What is the Y value when the point is on the X axis?
Any point on the X axis → Y = 0.
What is the X value of the green point?
The point is above the marking "2".
In which quadrant of the coordinate system is the point located?
Right (X+) and up (Y+) → first quadrant.
Which point represents the solution of the equation when Y = 0?
Y = 0 → a point that lies on the X axis.
The following graph shows a line. Which option describes it?
The line climbs from left to right → rising line.