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 point)
Responses
y=−3x+19
y is equal to negative 3 x plus 19
y=−2x+25
y is equal to negative 2 x plus 25
y=2x+21
y is equal to 2 x plus 21
y=2x+24
y = -2x + 25
step by step
To find the equation of the linear function that models the relationship shown in the table:
1. First, calculate the slope (m) of the linear function using two points from the table. Let's choose the points (2, 21) and (10, 5).
m = (y2 - y1) / (x2 - x1)
m = (5 - 21) / (10 - 2)
m = (-16) / 8
m = -2
2. Now that we have the slope (m), we can substitute it into the slope-intercept form of a linear equation: y = mx + b.
We have y = -2x + b.
3. To find the y-intercept (b), substitute one of the points into the equation. Let's use (2, 21).
21 = -2(2) + b
21 = -4 + b
b = 25
4. Now substitute the value of b back into the equation:
y = -2x + 25
Therefore, the equation that models the relationship shown in the table is y = -2x + 25.