The table represents some points on the graph of a line.
Which equation represents the same relationship?
The table represents some points on the graph of a line.
-42 -216
-16 -8
15 240
22 296
Which equation represents the same relationship?
y+42=8(x+216)
y+216=⅛(x+42)
y+216=8(x+42)
y+42=⅛(x+216)
To determine which equation represents the same relationship as the given table, we can find the slope between two points and then use the slope-intercept form of a line (y = mx + b) to write the equation.
Using the points (-42, -216) and (22, 296), we can find the slope:
slope = (296 - (-216)) / (22 - (-42))
slope = 512 / 64
slope = 8
So the equation representing the same relationship is:
y - (-216) = 8(x - (-42))
Simplifying this equation gives:
y + 216 = 8(x + 42)
Therefore, the equation that represents the same relationship as the given table is:
y + 216 = 8(x + 42)
To determine which equation represents the same relationship as the table, we can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept.
First, let's calculate the slope using the first two points (-42, -216) and (-16, -8):
m = (y2 - y1) / (x2 - x1)
= (-8 - (-216)) / (-16 - (-42))
= (208) / (26)
= 8
Now that we have the slope, let's determine the y-intercept by substituting one of the points into the equation:
-8 = 8(-16) + b
-8 = -128 + b
b = -8 + 128
b = 120
Therefore, the correct equation is y = 8x + 120, which can be rewritten as y = 8(x + 15). None of the given equation choices match this form, so none of them represent the same relationship as the table.
To determine which equation represents the same relationship as the table, we need to find the equation that relates the x-coordinate to the y-coordinate in a consistent manner.
Let's examine the values in the table:
x y
-42 -216
-16 -8
15 240
22 296
By comparing the values of x and y, we can see that the relationship between them is consistent. Every time x is multiplied by a certain factor, we get y.
Let's calculate the factor by looking at the differences between the x-values and the y-values:
For the first row, we have (-42,-216). By dividing y by x, we get -216 / -42 = 8.
For the second row, we have (-16, -8). The factor is -8 / -16 = 1/2.
For the third row, we have (15, 240). The factor is 240 / 15 = 16.
For the fourth row, we have (22, 296). The factor is 296 / 22 = 13.4545 (rounded).
Since the factor is not consistent, we can conclude that the relationship is not linear, and none of the given equations represent the same relationship as the table.