To determine the equation of a line that is parallel to the function graphed, we need to identify the slope of the function that is shown in the graph. Lines that are parallel have the same slope.
Let's analyze the provided options for their slopes:
-
y + 4 = (2/3)(x + 3)
Rearranging gives us:
\( y = \frac{2}{3}x - 4 + 2 \)
Therefore, the slope is \( \frac{2}{3} \). -
y = -\frac{3}{2}x + 7
The slope here is \( -\frac{3}{2} \). -
−2x − 3y = −15
Rearranging gives:
\( 3y = -2x + 15 \)
Therefore, \( y = -\frac{2}{3}x + 5 \)
The slope is \( -\frac{2}{3} \). -
y = -\frac{2}{3}x + 5
The slope here is \( -\frac{2}{3} \).
Based on the slopes calculated from the options:
- A line parallel to the original function must share the same slope as that function.
Make sure to compare the slopes to the slope of the given function from the graph to choose the correct answer. If the slope of the original function from the graph is, for example, \( -\frac{3}{2} \), then you would select the second option. However, without the specific slope from the provided graph, you must match the slope accordingly.
If the slope of the original function is not provided and you're unsure, you may consider which options have the same slope to determine which equation represents a parallel line.
Please give the slope from the graph to determine the correct answer accurately!