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Using the equation t=13n+7 , create a sequence that corresponds from the 1st term to the 5th term.

Responses

20, 33, 39, 59, 72

13, 26, 39, 50, 65

20, 33, 46, 59, 72

21, 22, 23, 24, 25

7 answers

To create a sequence using the equation \( t = 13n + 7 \), we can substitute values for \( n \) starting from 1 up to 5.

  1. For \( n = 1 \): \[ t = 13(1) + 7 = 13 + 7 = 20 \]

  2. For \( n = 2 \): \[ t = 13(2) + 7 = 26 + 7 = 33 \]

  3. For \( n = 3 \): \[ t = 13(3) + 7 = 39 + 7 = 46 \]

  4. For \( n = 4 \): \[ t = 13(4) + 7 = 52 + 7 = 59 \]

  5. For \( n = 5 \): \[ t = 13(5) + 7 = 65 + 7 = 72 \]

Putting it all together, the first five terms of the sequence are:

  • 20 (for \( n = 1 \))
  • 33 (for \( n = 2 \))
  • 46 (for \( n = 3 \))
  • 59 (for \( n = 4 \))
  • 72 (for \( n = 5 \))

Thus, the corresponding sequence is 20, 33, 46, 59, 72.

Therefore, the correct option is: 20, 33, 46, 59, 72.

Create a formula for the points (1,5), (2,7), (3,9), and (4,11).
Responses

y=−2x+3

y=−2x−3

y=2x+3

y=2x−3

To find the formula for the points (1, 5), (2, 7), (3, 9), and (4, 11), we can observe the relationship between the x and y values.

  1. Identify the pattern:
    • When \( x = 1 \), \( y = 5 \)
    • When \( x = 2 \), \( y = 7 \)
    • When \( x = 3 \), \( y = 9 \)
    • When \( x = 4 \), \( y = 11 \)

We can see that as \( x \) increases, \( y \) increases by 2 for each increase in \( x \). This suggests a linear relationship.

  1. Calculate the slope (m): The change in \( y \) divided by the change in \( x \): \[ m = \frac{\Delta y}{\Delta x} = \frac{7 - 5}{2 - 1} = \frac{2}{1} = 2 \]

  2. Form the equation: Using the slope-intercept form of the equation \( y = mx + b \), where \( m = 2 \).

  3. Find b (y-intercept): Using one of the points to find \( b \). Let's use the point (1, 5): \[ 5 = 2(1) + b \] \[ 5 = 2 + b \] \[ b = 5 - 2 = 3 \]

  4. Write the final equation: The linear equation that describes the given points is: \[ y = 2x + 3 \]

Therefore, the correct response is: y = 2x + 3.

When discussing the key features of a linear graph, which of the following statements is true?
Responses

The points will make a straight line.

The rate of change can vary along the graph.

The initial value is always zero.

The points always have positive values.

When discussing the key features of a linear graph, the following statement is true:

The points will make a straight line.

Explanation of Each Option:

  1. The points will make a straight line.

    • This is true for linear graphs. By definition, a linear function graphs to a straight line.

  2. The rate of change can vary along the graph.

    • This is false for a linear graph. The rate of change (slope) is constant in linear functions.

  3. The initial value is always zero.

    • This is false. The initial value (y-intercept) can be any number, not just zero.

  4. The points always have positive values.

    • This is false. Points on a linear graph can have both positive and negative values depending on the function.

Thus, the correct statement is: The points will make a straight line.

Use the image to answer the question.

What would the next point be on the graph?

Responses

(5,−2.5)

(0,−5)

(−4.5,−2.5)

(5,−3.5)

I currently can't see images, so I am unable to directly analyze the graph you're referring to. However, I can guide you on how to determine the next point based on a graph!

If you can describe the graph to me (mention the coordinates of existing points, the general direction of the line or curve—whether it's increasing or decreasing, etc.), I can help you identify what the next point might be.

Here are some steps you can take to estimate the next point:

  1. Identify the Pattern: Look at the coordinates of the existing points (x, y) and identify if there’s a consistent pattern or increase/decrease in the values of x and y.

  2. Calculate the Slope: If it's a straight line, calculate the slope (change in y divided by change in x) between known points to see if you can extend that to find the next point.

  3. Extrapolate: Based on the trend observed in the points, estimate where the next point is likely to be.

If you provide the details about the existing points or the nature of the graph, I can help more specifically!