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: [tex] m = \frac{y_{2} - y_{1} }{x_{2}-x_{1} } [/tex].
Substitute these points into the slope formula.
[tex] m = \frac{0 - (-2) }{6-10} = \frac{2}{-4} = \frac{1}{-2} [/tex]
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.
