Question

Decide whether each relation define y=(5)/(x-1)

Answer 1

To decide whether each relation defines y = 5/(x-1), substitute the given points into the equation, and check if the equation holds true for those points.

Step-by-step explanation:

The given relation is y = 5/(x-1). To decide whether each relation defines this equation, we need to substitute the given points into the equation and check if the equation holds true for those points.

Let's check the given points:

• For (1,5): y = 5/(1-1) = 5/0 which is undefined. This point does not define the equation.
• For (2,10): y = 5/(2-1) = 5/1 = 5. This point satisfies the equation.
• For (3,7): y = 5/(3-1) = 5/2 = 2.5. This point does not satisfy the equation.
• For (4,14): y = 5/(4-1) = 5/3 ≈ 1.67. This point does not satisfy the equation.

Based on the given points, only (2,10) satisfies the equation y = 5/(x-1), so we can say that the relation partially defines the equation.

Answer 2

The points given do not define the relation y=5/(x-1) because substituting the x-values from the points into the equation does not consistently result in the corresponding y-values, notably due to issues with division by zero.

Step-by-step explanation:

The student has asked whether the points (1,5), (2,10), (3,7), and (4,14) define the relation y = 5/(x-1). To determine this, each x-value from the points can be substituted into the relation to see if the corresponding y-value is produced.

The dependence of y on x is observed by mapping these values on a graph. If the points do not satisfy the relation, then the relation does not define all the points.

To illustrate, let's test the first point (1,5), substituting x=1 into the relation gives y=5/(1-1), which is undefined because of division by zero. Thus, (1,5) does not define the relation y=5/(x-1). We would continue this process for each point to conclude whether the given relation defines all the points on the table.

When analyzing relationships in a course, we often encounter equations like linear equations of the form y = b + mx, which express graphically the dependence of y on the independent variable x.