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Does a graph showing direct proportion always have to be a straight line?
Assuming both the scales on the graph are linear (that is to say that the numbers go up evenly) then YES, a graph which shows direct proportion must be a straight line. It must also pass through the origin (0,0). A straight line which does not pass through the origin is NOT showing direct proportion. Duncan
What is the equation of the line whose graph passes through the origin and has a slope of 1?
Slope = 1Y-intercept = 0Y = X
What point on the graph could be the fourth vertex of the parallelogram?
the origin is the point in the graph that can be fourth vertex
What is the location of the origin on a line graph?
(0, 0)
What mathematical relationship between variables is suggested by a graph showing a half-parabola?
inverse linear or quadratic
Does the graph of a direct variation pass through the origin?
yes, a graph of a direct variation must pass through the origin because direct variation is always in form of y=mx where x and y are variables and m is a constant.
What does the graph of an inverse variation look like?
A hyperbola.
How can you tell if a line is the graph of a direct variation?
It is a straight line passing through the origin.
How can you tell of a line is the graph of direct variation?
It is a straight line passing through the origin.
What is general shape of a graph of an inverse variation relationship?
Cartestian plane
Why does the graph of an equation expressing direct variation always pass through the origin?
For a direct variation, y=kx where k is the constant of variation if x =0 then y=0 and the graph of y=kx passes through the origin. -Indiana Prentice Hall Algebra 2 Text Book.
How can you tell if one function is the inverse of another?
draw them both out on a graph and then draw the line y=x through the origin. If one function is a reflection of the other, it is the inverse
How does the constant of variation affects the appearance of the graph of a direct variation function?
The formula direct variation is xk=y, where k is the constant of variation.Direct variation functions always pass through the origin. Direct variation functions are linear functions (goes in a straight line), except that they pass through the origin. Regular linear functions don't pass through the origin. That is the only difference.
What is the y-intercept of the graph of a direct variation equation?
Graphs of direct variation pass through the origin so the y-intercept would be 0.
How do you determine direct and inverse proportion on graphs?
If the variables x and y are in direct proportion then the graph of y against x is a straight line through the origin. If the variables x and y are in inverse proportion then the graph of y against x is a rectangular hyperbola. Alternatively, the graph of y against 1/x (or 1/y against x) is a straight line through the origin.
Is every relationship whose graph passes through the origin direct variation?
No, not every relationship whose graph passes through the origin represents direct variation. Direct variation specifically means that the relationship can be expressed in the form ( y = kx ), where ( k ) is a non-zero constant. While a graph passing through the origin indicates a proportional relationship, it can also represent other types of relationships, such as quadratic or polynomial functions, if they contain additional terms. Therefore, the key characteristic of direct variation is the constant ratio between ( y ) and ( x ), not just the point of intersection at the origin.
How can you know if a graph represents a proportional relationship?
It is a relationship of direct proportion if and only if the graph is a straight line which passes through the origin. It is an inverse proportional relationship if the graph is a rectangular hyperbola. A typical example of an inverse proportions is the relationship between speed and the time taken for a journey.
