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`?
To find the slope of the linear function `g`, we can use the formula:
\[m = \frac{y_2 - y_1}{x_2 - x_1}.\]
Using the given points \((2, -1)\) and \((-2, 7)\), we get:
\[m = \frac{7 - (-1)}{-2 - 2} = \frac{8}{-4} = -2.\]
So, the slope of the graph `g` is \(-2\).
To find the y-intercept of the linear function `g`, we can plug one of the points, say \((2, -1)\), into the point-slope form of the equation of a line:
\[y - y_1 = m(x - x_1).\]
Substitute the values \((x_1, y_1) = (2, -1)\) and \(m = -2\):
\[y - (-1) = -2(x - 2).\]
Simplify:
\[y + 1 = -2x + 4.\]
\[y = -2x + 3.\]
Therefore, the y-intercept of the graph `g` is \(3\).