Select the equation of a line that is parallel to the function graphed below: It is a double arrow, the top of the arrow reaching into the top right part of the graph, the top middle part of the arrow just BARELY under the 5. The end of the middle of the double arrow is halfway in the middle of -5 and -10. It doesn't show where the very top of the arrows are, but we can see the top middle and the bottom middle.

Question

A. y = - 2/3 x + 5
B. y + 4 = 2/3 (x + 3)
C. -2x - 3y = -15
D. y = - 3/2 x + 7

Answer 1

To determine which equation represents a line that is parallel to the given function, we need to identify the slope of the line from the function that is graphed. Parallel lines have the same slope.

From your description, it seems that the graphed line has a positive slope because it rises as it moves from left to right. You also mention that the line has a double arrow pointing towards the top right, which confirms that it is indeed ascending.

Next, let's examine the slopes of the options provided:

A. \( y = -\frac{2}{3} x + 5 \) has a slope of \( -\frac{2}{3} \) (not parallel). B. \( y + 4 = \frac{2}{3} (x + 3) \) can be rewritten as \( y = \frac{2}{3} x + \frac{2}{3} \cdot 3 - 4 = \frac{2}{3} x + 2 - 4 = \frac{2}{3} x - 2 \); this has a slope of \( \frac{2}{3} \) (could be parallel if the slope matches). C. Rearranging \( -2x - 3y = -15 \) gives \( 3y = -2x + 15 \) or \( y = -\frac{2}{3}x + 5 \); this has a slope of \( -\frac{2}{3} \) (not parallel). D. \( y = -\frac{3}{2} x + 7 \) has a slope of \( -\frac{3}{2} \) (not parallel).

Looking at the options, only option B has the same positive slope as indicated by your description, with a slope of \( \frac{2}{3} \).

Therefore, the correct equation of a line that is parallel to the function graphed is: B. \( y + 4 = \frac{2}{3} (x + 3) \).