Question

3. Use the table of values below to write its linear function in slope-intercept form. Then, sketch a graph of the function

Answer 1

The slope-intercept form of a line is:

y = mx + b

where m is the slope and b the y-intercept

The slope of a line that passes through points (x1, y1) and (x2, y2) is computed as follows:

`m\text{ = }(y_2-y_1)/(x_2-x_1)`

Replacing with (4, 4) and (20, 12):

`m=(12-4)/(20-4)=(8)/(16)=(1)/(2)`

Replacing into the general equation with m = 1/2 and point (20,12) we get:

12 = 1/2(20) + b

12 = 10 + b

12 - 10 = b

2 = b

Then, the equation is: y = 1/2x+ 2

And the graph is: