Which graph accurately depicts the correct formula for the points (1,5)

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.
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1 2 three or four

GPT-4o mini · Answer

To determine which graph depicts the correct relationship for the points (1,5), (2,7), (3,9), and (4,11), let's first identify any patterns.

The points can be outlined as follows:

(1, 5)
(2, 7)
(3, 9)
(4, 11)

We can observe that as $x$ increases by 1, $y$ increases by 2. This indicates a linear relationship.

To extract the formula, we can identify the slope ( $m$ ):

$m = \frac{c h a n g e : i n : y}{c h a n g e : i n : x} = \frac{7 - 5}{2 - 1} = 2$

Now, we can find the y-intercept ( $b$ ), which can be determined using one of the points. Substituting $x = 1$ and $y = 5$ into the slope-intercept form $y = m x + b$ :

$5 = 2 (1) + b ⟹ b = 5 - 2 = 3$

Thus, the equation that represents this relationship is:

$y = 2 x + 3$

Now, you need to choose the graph that represents this line. Look for a line that passes through the points (1,5), (2,7), (3,9), and (4,11) consistently, showing the given linear equation $y = 2 x + 3$ .

If you have the graphs available, select the one that meets this criterion.