A straight line passing through the origin represents a ________________________ relationship. However,not all straight lines pass through the origin. Such lines represent relationships that are not proportional.
Question
A straight line passing through the origin represents a ________________________ relationship. However,not all straight lines pass through the origin. Such lines represent relationships that are not proportional.
Solution
A straight line passing through the origin represents a proportional relationship. This is because the ratio between the y and x coordinates for any point on the line is constant.
Step 1: Understand the concept of a proportional relationship. In a proportional relationship, the ratio between two variables is constant. This means that for any given point on the line, the value of one variable divided by the value of the other variable will always be the same.
Step 2: Apply this concept to a line passing through the origin. The origin of a graph is the point where the x and y coordinates are both zero. If a line passes through this point, it means that when both variables are zero, the relationship still holds. This is a key characteristic of a proportional relationship.
Step 3: Understand that not all straight lines represent proportional relationships. If a line does not pass through the origin, it means that the relationship between the variables is not constant when they are both zero. Therefore, such lines represent relationships that are not proportional.
So, in conclusion, a straight line passing through the origin represents a proportional relationship, while lines that do not pass through the origin represent relationships that are not proportional.
Similar Questions
Graph the line that passes through the coordinates shown and determine which statement is true. A. The line that passes through the given coordinates represents a proportional relationship because the line passes through the origin. B. The line that passes through the given coordinates does not represent a proportional relationship because the line passes through the origin. C. The line that passes through the given coordinates does not represent a proportional relationship because the line does not pass through the origin. D. The line that passes through the given coordinates represents a proportional relationship because the line does not pass through the origin.
The origin is the point where the two _________ meet in a coordinate plane.❖ It is represented by the ordered pair (0, 0).• Since we need two points to graph a line, we need to know a _________ on the relationship’s________ other than the origin to graph a proportional relationship.• When graphing proportional relationships, the origin corresponds to the ____________ point.Proportional relationships can be represented in many ways:a ______________ description, an ____________, a table and a graph.
Line m passes through the points (3, 7) and (6, 12) while line n passes through the points (-5, 1) and (-2, 6).Which statement accurately describes the relationship between the two lines?A.Lines m and n have the same slope so they are parallel.B.Lines m and n have opposite reciprocal slopes so they are perpendicular.C.Lines m and n have the same slope so they are perpendicular.D.Lines m and n have opposite reciprocal slopes so they are parallel.
12. All data points falling along a straight line is called:*2 pointsLinear relationshipNon linear relationshipResidualScatter diagram
Which definition matches the term Line?Group of answer choicesa set of points extending forever in two opposite directionsthe intersection of the x-axis and y-axis on a coordinate plane; labeled with ordered pair, (0, 0)the ratio of any y-value to its corresponding x-value in a proportional relationship
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