Question

In the graph, the y-intercept of the function is (0,
graph:
(5,2)
(-5,-6)

Answer 1

It appears you're describing a graph with two points: (5, 2) and (-5, -6), while also mentioning the y-intercept. However, the y-intercept is the point at which a function intersects the y-axis, which occurs when \(x = 0\).

To find the y-intercept, we typically would need either the equation of the line or to determine the slope of the line connecting the two points you've provided.

Let's find the slope \(m\) of the line using the two points \((5, 2)\) and \((-5, -6)\):

1. Use the slope formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
where \((x_1, y_1) = (5, 2)\) and \((x_2, y_2) = (-5, -6)\).

\[
m = \frac{-6 - 2}{-5 - 5} = \frac{-8}{-10} = \frac{4}{5}
\]

2. Now, use one of the points to find the equation of the line. We'll use the point-slope form \(y - y_1 = m(x - x_1)\).

Using point \((5, 2)\):
\[
y - 2 = \frac{4}{5}(x - 5)
\]

Simplifying this:
\[
y - 2 = \frac{4}{5}x - 4
\]
\[
y = \frac{4}{5}x - 2
\]

3. Now we can find the y-intercept by substituting \(x = 0\):
\[
y = \frac{4}{5}(0) - 2 = -2
\]

So, the y-intercept is \((0, -2)\).

If you have any further questions or if the graph information needs to be interpreted differently, please let me know!