Question

(18, 10) (6, -3) write the equation of the linear function represented by the table

Answer 1

To write the equation of the linear function represented by the table, we need to find the slope (m) and the y-intercept (b) of the line.

We can use the formula for slope (m) to find it:
m = (change in y) / (change in x)
m = (-3 - 10) / (6 - 18)
m = -13 / (-12)
m = 13/12

Next, we can use the slope-intercept form of a linear equation (y = mx + b) and substitute the values of one of the points (18, 10).

10 = (13/12)(18) + b

Now, we solve for b:

10 = (13/12)(18) + b
10 = (39/4) + b
10 - (39/4) = b
(40 - 39/4) / 4 = b
(160 - 39) / 4 = b
121 / 4 = b
b = 121/4

Therefore, the equation of the linear function represented by the table is:

y = (13/12)x + 121/4