X(-1,-3), Y(4,8) find the rate of cha get and the initial value of the linear function given as table of values. The rate of change is m= , and the intial value is b .
To find the rate of change, we can use the formula for slope:
m = (y2 - y1) / (x2 - x1)
In this case, the coordinates given are:
Point X: (-1, -3)
Point Y: (4, 8)
Plugging the coordinates into the formula, we get:
m = (8 - (-3)) / (4 - (-1))
= (8 + 3) / (4 + 1)
= 11 / 5
So, the rate of change (m) is 11/5.
To find the initial value (b), we can use the slope-intercept form of a linear equation:
y = mx + b
Plugging in the slope value we just found (m = 11/5) and using one of the points (X or Y), let's use point X (-1, -3), we can solve for b:
-3 = (11/5)(-1) + b
-3 = -11/5 + b
To get rid of the fraction, we can multiply both sides by 5:
-15 = -11 + 5b
To isolate b, we subtract -11 from both sides:
-15 + 11 = 5b
-4 = 5b
To solve for b, we divide both sides by 5:
b = -4/5
Therefore, the initial value (b) is -4/5.