The graph of linear function `g` passes through the points `\left(2,\ -1\right)`and `\left(-2,\ 7\right),`as shown. What are the slope and y-intercept of the graph g?

Answer 1

To find the slope of the linear function `g`, we first calculate the change in y divided by the change in x between the two points:

Slope = (Change in y) / (Change in x)
Slope = (7 - (-1)) / (-2 - 2) = 8 / -4 = -2

Now that we have the slope, we can use one of the points to find the y-intercept. Let's use the point (2,-1):

y = mx + b
-1 = -2(2) + b
-1 = -4 + b
b = 3

Therefore, the slope of the graph `g` is -2 and the y-intercept is 3.