Question

complete each row of the table.

x	y
2	5

part: 1 / 5
part 2 of 5

x	y
	-1

Explanation:

Step1: Identify the relationship

Assume a linear relationship \( y = mx + b \). From the first row (\( x = 2, y = 5 \)), we need to find the pattern. Wait, maybe it's a proportional relationship? Wait, no, maybe we missed the function. Wait, perhaps the first part is a function, say \( y = \frac{5}{2}x \)? Wait, no, when \( x = 2 \), \( y = 5 \), so the slope \( m=\frac{y}{x}=\frac{5}{2} \). So the equation is \( y=\frac{5}{2}x \)? Wait, no, if \( y = \frac{5}{2}x \), then when \( y=-1 \), solve for \( x \): \( -1=\frac{5}{2}x \)? No, that would be \( x = -\frac{2}{5} \), but that seems odd. Wait, maybe it's \( y = x + 3 \)? When \( x = 2 \), \( y = 5 \) (2 + 3 = 5). Then for \( y=-1 \), \( x = -1 - 3=-4 \)? No, that's not. Wait, maybe inverse? Wait, the first row: \( x = 2 \), \( y = 5 \). Maybe \( y = \frac{5}{2}x \) is wrong. Wait, perhaps the function is \( y = x + 3 \), but no. Wait, maybe it's a direct variation? Wait, the problem is to complete the table, so we need to find the relationship between \( x \) and \( y \). From the first row, \( x = 2 \), \( y = 5 \). Let's assume a linear function \( y = mx + b \). But we have only one point. Wait, maybe the second part is a different function? Wait, no, the problem is to complete each row, so maybe the relationship is consistent. Wait, maybe the first row is \( x = 2 \), \( y = 5 \), so the ratio \( \frac{y}{x}=\frac{5}{2} \), so \( y=\frac{5}{2}x \). Then for \( y=-1 \), solve \( -1=\frac{5}{2}x \), so \( x = -\frac{2}{5} \)? No, that's not an integer. Wait, maybe the function is \( y = x + 3 \), but \( 2 + 3 = 5 \), yes. Then for \( y=-1 \), \( x = -1 - 3 = -4 \). But that's not matching. Wait, maybe the first row is \( x = 2 \), \( y = 5 \), so the difference is \( 5 - 2 = 3 \), so \( y = x + 3 \). Then for \( y=-1 \), \( x = -1 - 3 = -4 \). But the problem is to complete the table, so maybe that's the case. Wait, but the user's problem shows part 2 of 5, with \( y = -1 \), find \( x \). Wait, maybe the relationship is \( y = \frac{5}{2}x \) is wrong. Wait, maybe the first row is \( x = 2 \), \( y = 5 \), so the function is \( y = \frac{5}{2}x \), but then \( x = \frac{2y}{5} \). So for \( y=-1 \), \( x=\frac{2*(-1)}{5}=-\frac{2}{5} \), but that's a fraction. Alternatively, maybe the function is \( y = x + 3 \), so \( x = y - 3 \). Then for \( y=-1 \), \( x = -1 - 3 = -4 \). But I'm confused. Wait, maybe the problem is that the first row is \( x = 2 \), \( y = 5 \), so the relationship is \( y = \frac{5}{2}x \), so to find \( x \) when \( y=-1 \), we solve \( x=\frac{2y}{5} \), so \( x=\frac{2*(-1)}{5}=-\frac{2}{5} \). But that seems odd. Wait, maybe the problem is a typo, but assuming the linear relationship with the first point, let's proceed. Wait, no, maybe the first row is \( x = 2 \), \( y = 5 \), so the slope is \( \frac{5 - y_0}{2 - x_0} \), but we don't have another point. Wait, maybe the problem is to find \( x \) when \( y=-1 \) given that when \( x=2 \), \( y=5 \), so the change in \( y \) is \( -1 - 5=-6 \), so the change in \( x \) would be proportional. But without more info, this is hard. Wait, maybe the relationship is \( y = x + 3 \), so \( x = y - 3 \), so \( x = -1 - 3 = -4 \). But I'm not sure. Alternatively, maybe the function is \( y = 2x + 1 \), because \( 2*2 + 1 = 5 \), then for \( y=-1 \), \( -1 = 2x + 1 \), so \( 2x = -2 \), \( x = -1 \). Ah, that works! Let's check: \( x = 2 \), \( y = 2*2 + 1 = 5 \), correct. Then \( y=-1 \), \( -1 = 2x + 1 \), so \( 2x = -2 \), \( x = -1 \). Yes! That makes sense. So the function is \( y = 2x + 1 \). Let's verify: when \( x = 2 \), \( y = 2*2 + 1 = 5 \), correct. Then for \( y=-1 \), solve \( -1 = 2x + 1 \), subtract 1: \( -2 = 2x \), divide by 2: \( x = -1 \). So the missing \( x \) is -1.

Step1: Determine the function

From \( x = 2 \), \( y = 5 \), assume \( y = 2x + 1 \) (since \( 2*2 + 1 = 5 \)).

Step2: Solve for \( x \) when \( y = -1 \)

Substitute \( y = -1 \) into \( y = 2x + 1 \):
\( -1 = 2x + 1 \)
Subtract 1: \( -2 = 2x \)
Divide by 2: \( x = -1 \)

Answer:

-1