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Create a formula for the points (1,5)

, (2,7)
, (3,9)
, and (4,11)
.(1 point)
Responses

y=−2x+3

y=2x−3

y=2x+3

y=−2x−3

3 answers

To find the equation of the line that passes through the points (1, 5), (2, 7), (3, 9), and (4, 11), we can first determine the slope (m) of the line using any two of the given points.

Let's use the points (1, 5) and (2, 7).

The formula for the slope (m) is: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Substituting the values: \[ m = \frac{7 - 5}{2 - 1} = \frac{2}{1} = 2 \]

Now that we have the slope, we can use the point-slope form of the equation of a line: \[ y - y_1 = m(x - x_1) \]

Using the point (1, 5): \[ y - 5 = 2(x - 1) \]

Now, simplify the equation: \[ y - 5 = 2x - 2 \] \[ y = 2x + 3 \]

Thus, the formula for the points is: \[ \boxed{y = 2x + 3} \]

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

The initial value is always zero.

The rate of change can vary along the graph.

The points always have positive values.

The points will make a straight line.

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

The points will make a straight line.

Linear graphs are characterized by a constant rate of change and will always form a straight line when plotted on a coordinate plane.

So the correct response is: The points will make a straight line.