Question

Determine the linear function that goes through the points (10,-2) and (6,0). Write answer in slope intercept form

Answer 1

Hello!

To find the the function that goes through the points (10, -2) and (6, 0), we need to use the slope formula, and then find the y-intercept.

The slope formula is:
`m = (y_(2) - y_(1) )/(x_(2)-x_(1) )`.

Substitute these points into the slope formula.

`m = (0 - (-2) )/(6-10) = (2)/(-4) = (1)/(-2)`

The slope of the function is -1/2. Then, we need to find the y-intercept. Slope-intercept form is: y = mx + b. In this equation, m is the slope, which is -1/2, and b is the y-intercept. To find the y-intercept, we substitute the slope, and an ordered pair and solve.

0 = -1/2(6) + b

0 = -3 + b (add 3 to both sides)

b = 3

Therefore, the linear function is y = -1/2x - 3.