Which equation of the linear function models the relationship shown in the table.
| x | y |
| 2|21|
|4 |17|
| 5|15|
| 8| 9 |
|10| 5 |
1.y=−3x+19
2.y=−2x+25
3.y=2x+24
4.y=2x+21
show work
To find the equation of the linear function that models the relationship shown in the table, we will first find the slope (m) using two points on the line. Let's use the points (2, 21) and (10, 5):
m = (y2 - y1) / (x2 - x1)
m = (5 - 21) / (10 - 2)
m = -16 / 8
m = -2
Next, we can use the slope (m) and one point from the table to find the y-intercept (b). Let's use the point (2, 21):
y = mx + b
21 = -2(2) + b
21 = -4 + b
b = 21 + 4
b = 25
Therefore, the equation of the linear function that models the relationship shown in the table is:
y = -2x + 25
So, the correct answer is:
2. y = -2x + 25