Question

Which graph accurately depicts the correct formula for the points (1,5), (2,7), (3,9), and (4,11)?(1 point)
Responses

A line passes through two points plotted on a coordinate plane.
Image with alt text: A line passes through two points plotted on a coordinate plane.

A line passes through two points plotted on a coordinate plane.
Image with alt text: A line passes through two points plotted on a coordinate plane.

A line passes through two points plotted on a coordinate plane.
Image with alt text: A line passes through two points plotted on a coordinate plane.

A line passes through two points plotted on a coordinate plane.
Image with alt text: A line passes through two points plotted on a coordinate plane.
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Answer 1

To determine which graph accurately represents the points (1, 5), (2, 7), (3, 9), and (4, 11), we first need to analyze the relationship between the x and y coordinates of the given points.

To check for a linear relationship, we can find the differences in y for the differences in x:

- From (1, 5) to (2, 7): 7 - 5 = 2 (increase of 2)
- From (2, 7) to (3, 9): 9 - 7 = 2 (increase of 2)
- From (3, 9) to (4, 11): 11 - 9 = 2 (increase of 2)

Since the change in y (2) is consistent whenever x increases by 1, this indicates a linear relationship.

To write the equation of the line, we can find the slope (m). The slope between any two points can be calculated as:

\[ m = \frac{\Delta y}{\Delta x} = \frac{2}{1} = 2 \]

Using point (1, 5), we apply the point-slope form of the equation of a line, which is:

\[ y - y_1 = m(x - x_1) \]

Plugging the values into the equation:

\[ y - 5 = 2(x - 1) \]

Distributing:

\[ y - 5 = 2x - 2 \]
\[ y = 2x + 3 \]

Now, the correct formula for the relationship between x and y in these points is \( y = 2x + 3 \).

The graph that represents this equation will be a straight line that passes through the points (1, 5), (2, 7), (3, 9), and (4, 11).

Since I cannot see the graphs, you should look for a straight line that intersects these specified points on the coordinate plane.