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Using the equation t=13n+7

, create a sequence that corresponds from the 1st term to the 5th term.(1 point)
Responses

20, 33, 39, 59, 72
20, 33, 39, 59, 72

21, 22, 23, 24, 25
21, 22, 23, 24, 25

20, 33, 46, 59, 72
20, 33, 46, 59, 72

13, 26, 39, 50, 65

7 answers

To create a sequence using the equation \( t = 13n + 7 \), we will evaluate the equation for \( n = 1 \) through \( n = 5 \):

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

Thus, the sequence corresponding to the first five terms is:

20, 33, 46, 59, 72

So the correct response is:

20, 33, 46, 59, 72

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

y=−2x−3
y equals negative 2 x minus 3

y=−2x+3
y equals negative 2 x plus 3

y=2x−3
y equals 2 x minus 3

y=2x+3

To find the formula that represents the points (1,5), (2,7), (3,9), and (4,11), we can first observe the pattern of the y-values as x increases.

Calculating the differences between the y-values:

  • When \( x = 1 \), \( y = 5 \)
  • When \( x = 2 \), \( y = 7 \)
  • When \( x = 3 \), \( y = 9 \)
  • When \( x = 4 \), \( y = 11 \)

We can see that for each increase of 1 in \( x \), \( y \) increases by 2. This indicates that the slope \( m \) is \( 2 \).

We can use the point-slope form of the linear equation \( y = mx + b \):

  1. Using the slope \( m = 2 \):

Next, we need to find the y-intercept \( b \). We can use one of the points to do this. Let's use the point \( (1, 5) \):

\[ 5 = 2(1) + b \] \[ 5 = 2 + b \] \[ b = 5 - 2 = 3 \]

Thus, the equation becomes: \[ y = 2x + 3 \]

So the correct response is:

y = 2x + 3.

When discussing the key features of a linear graph, which of the following statements is true?(1 point)
Responses

The points always have positive values.
The points always have positive values.

The points will make a straight line.
The points will make a straight line.

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

The initial value is always zero.

The true statement regarding the key features of a linear graph is:

The points will make a straight line.

This is because a linear graph represents a linear relationship between the variables, resulting in a straight line when plotted on a coordinate plane. The other statements are not necessarily true:

  • The points always have positive values: This is not true, as linear graphs can have points in any quadrant, including negative values.
  • The rate of change can vary along the graph: This is false for a linear graph, as the rate of change (slope) is constant throughout the graph.
  • The initial value is always zero: This is false; the initial value (y-intercept) can be any value, not just zero.

Thus, the correct response is:

The points will make a straight line.

Use the image to answer the question.

Four points are plotted on a coordinate plane. The x-axis ranges from 0 to 6 in increments of 1. The y-axis ranges from negative 6 to 0 in increments of 1.

What would the next point be on the graph?

(1 point)
Responses

(5,−2.5)
left parenthesis 5 comma negative 2.5 right parenthesis

(0,−5)
left parenthesis 0 comma negative 5 right parenthesis

(−4.5,−2.5)
left parenthesis negative 4.5 comma negative 2.5 right parenthesis

(5,−3.5)
left parenthesis 5 comma negative 3.5 right parenthesis
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Without the image, I can only provide general guidance on how to determine the next point in a plotted sequence.

To determine the next point in a sequence of points on a graph, you would typically look for a pattern in the x and y coordinates of the existing points.

Here’s how you can approach it:

  1. Identify the coordinates of the existing points to see if there is a visible linear pattern, or if they appear to follow a specific function or trend.

  2. Examine the increments of both the x-values and the y-values: If the x-values increase steadily (e.g., by 1 or another constant value), you can predict the next x-value. Then you can determine the corresponding y-value based on the pattern you observe.

  3. Choose the point that fits the observed pattern from the given options.

If you can describe the coordinates of the points already plotted, I would be able to help you deduce the next point more accurately. Otherwise, I would suggest selecting the option that seems to logically continue the trend based on any visible patterns in the coordinates.